Your data matches 17 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000993
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => 2
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 3
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => 2
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => 1
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 2
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => 2
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => 2
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => [2]
 => 1
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => [3]
 => 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => 1
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => 1
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => 1
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => 1
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => 2
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => 2
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => 2
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => 1
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => 2
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => 1
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 1
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 1
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 1
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 1
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 1
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 2
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => 1
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 3
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => 2
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => 2
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => 2
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => 2
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => [2]
 => 1
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [[4,4,1],[3]]
 => [3]
 => 1
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => 1
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => 1
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => 1
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3,1],[1,1]]
 => [1,1]
 => 2
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3,1],[1,1]]
 => [1,1]
 => 2
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1]]
 => [1,1]
 => 2
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => [2]
 => 1
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1]]
 => [1,1]
 => 2
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => [2]
 => 1
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3,1],[2]]
 => [2]
 => 1
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3,1],[2]]
 => [2]
 => 1
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St000298
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000298: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 25%
Values
[2,1,3,4] => [2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => 2
[2,3,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
 => 1
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 2
[1,3,4,2,5] => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[2,1,3,4,5] => [2,1,3,4,5] => [3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 3
[2,1,3,5,4] => [2,1,3,5,4] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2
[2,1,4,3,5] => [2,1,4,3,5] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => ? = 1
[2,1,5,3,4] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2
[2,1,5,4,3] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2
[2,3,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[2,3,1,5,4] => [3,2,1,5,4] => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1
[2,3,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[2,3,5,1,4] => [4,2,5,1,3] => [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1
[2,3,5,4,1] => [5,2,4,3,1] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1
[2,4,1,3,5] => [3,4,1,2,5] => [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 1
[2,4,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[2,4,5,1,3] => [4,5,3,1,2] => [5,1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2
[2,4,5,3,1] => [5,4,3,2,1] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 2
[3,1,2,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[3,1,4,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[3,2,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[3,2,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,1,2,3,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,1,3,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,2,1,3,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,2,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,3,1,2,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,3,2,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
 => ? = 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 3
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(1,10),(1,15),(2,8),(2,11),(2,15),(3,7),(3,8),(3,9),(4,7),(4,10),(4,11),(4,15),(5,17),(7,12),(7,13),(7,16),(8,13),(8,16),(9,12),(9,16),(10,12),(10,14),(11,5),(11,13),(11,14),(12,18),(13,17),(13,18),(14,17),(14,18),(15,5),(15,14),(15,16),(16,17),(16,18),(17,6),(18,6)],19)
 => ? = 1
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,12),(1,18),(1,20),(2,11),(2,13),(2,17),(2,18),(3,14),(3,15),(3,17),(3,18),(3,20),(4,9),(4,13),(4,15),(4,20),(5,7),(5,9),(5,12),(5,17),(6,7),(6,10),(6,11),(6,14),(6,20),(7,24),(7,25),(7,26),(9,19),(9,26),(10,24),(10,25),(11,21),(11,24),(11,25),(12,24),(12,26),(13,19),(13,21),(14,16),(14,24),(14,25),(15,16),(15,19),(15,21),(16,22),(16,23),(17,19),(17,25),(17,26),(18,21),(18,24),(18,26),(19,23),(20,16),(20,21),(20,25),(20,26),(21,22),(21,23),(22,8),(23,8),(24,22),(25,22),(25,23),(26,22),(26,23)],27)
 => ? = 1
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [2,1,4,6,5,3] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
 => ? = 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,6),(3,7),(3,9),(3,11),(4,6),(4,7),(4,8),(4,10),(6,14),(6,19),(7,13),(7,15),(7,19),(8,13),(8,19),(9,13),(9,16),(9,19),(10,14),(10,15),(10,19),(11,14),(11,15),(11,16),(12,16),(12,19),(13,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,5),(18,5),(19,17),(19,18)],20)
 => ? = 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,21),(1,22),(2,11),(2,13),(2,18),(3,12),(3,14),(3,18),(4,8),(4,9),(4,13),(4,18),(5,8),(5,10),(5,14),(5,18),(6,9),(6,10),(6,11),(6,12),(8,17),(8,19),(9,15),(9,19),(9,20),(10,1),(10,16),(10,19),(10,20),(11,15),(11,20),(12,16),(12,20),(13,15),(13,19),(14,16),(14,17),(15,21),(16,21),(16,22),(17,22),(18,17),(18,19),(18,20),(19,21),(19,22),(20,21),(20,22),(21,7),(22,7)],23)
 => ? = 2
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [2,1,6,5,4,3] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
 => ? = 2
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
 => ? = 4
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [3,2,4,5,1,6] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,17),(2,7),(2,13),(3,9),(3,11),(3,13),(4,1),(4,8),(4,11),(4,13),(5,7),(5,8),(5,9),(7,16),(8,12),(8,16),(8,17),(9,12),(9,16),(10,14),(11,10),(11,12),(11,17),(12,14),(12,15),(13,16),(13,17),(14,6),(15,6),(16,15),(17,14),(17,15)],18)
 => ? = 3
[2,1,3,5,4,6] => [2,1,3,5,4,6] => [3,2,4,6,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,7),(1,8),(1,9),(2,9),(2,10),(2,12),(3,8),(3,10),(3,11),(4,7),(4,11),(4,12),(5,17),(7,14),(7,15),(8,13),(8,14),(9,13),(9,15),(10,13),(10,16),(11,5),(11,14),(11,16),(12,5),(12,15),(12,16),(13,18),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,6),(18,6)],19)
 => ? = 1
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,6,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,5,6,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,4,3,5,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,4,5,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,5,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,5,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,1,4,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,2,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,4,1,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,4,2,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
Description
The order dimension or Dushnik-Miller dimension of a poset. This is the minimal number of linear orderings whose intersection is the given poset.
Matching statistic: St000307
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000307: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 12%
Values
[2,1,3,4] => [2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 2
[2,3,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
 => 1
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 2
[1,3,4,2,5] => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[2,1,3,4,5] => [2,1,3,4,5] => [3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 3
[2,1,3,5,4] => [2,1,3,5,4] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2
[2,1,4,3,5] => [2,1,4,3,5] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => ? = 1
[2,1,5,3,4] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2
[2,1,5,4,3] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2
[2,3,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[2,3,1,5,4] => [3,2,1,5,4] => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1
[2,3,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[2,3,5,1,4] => [4,2,5,1,3] => [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1
[2,3,5,4,1] => [5,2,4,3,1] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1
[2,4,1,3,5] => [3,4,1,2,5] => [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 1
[2,4,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[2,4,5,1,3] => [4,5,3,1,2] => [5,1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2
[2,4,5,3,1] => [5,4,3,2,1] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 2
[3,1,2,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[3,1,4,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[3,2,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[3,2,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,1,2,3,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,1,3,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,2,1,3,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,2,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,3,1,2,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,3,2,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
 => ? = 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 3
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(1,10),(1,15),(2,8),(2,11),(2,15),(3,7),(3,8),(3,9),(4,7),(4,10),(4,11),(4,15),(5,17),(7,12),(7,13),(7,16),(8,13),(8,16),(9,12),(9,16),(10,12),(10,14),(11,5),(11,13),(11,14),(12,18),(13,17),(13,18),(14,17),(14,18),(15,5),(15,14),(15,16),(16,17),(16,18),(17,6),(18,6)],19)
 => ? = 1
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,12),(1,18),(1,20),(2,11),(2,13),(2,17),(2,18),(3,14),(3,15),(3,17),(3,18),(3,20),(4,9),(4,13),(4,15),(4,20),(5,7),(5,9),(5,12),(5,17),(6,7),(6,10),(6,11),(6,14),(6,20),(7,24),(7,25),(7,26),(9,19),(9,26),(10,24),(10,25),(11,21),(11,24),(11,25),(12,24),(12,26),(13,19),(13,21),(14,16),(14,24),(14,25),(15,16),(15,19),(15,21),(16,22),(16,23),(17,19),(17,25),(17,26),(18,21),(18,24),(18,26),(19,23),(20,16),(20,21),(20,25),(20,26),(21,22),(21,23),(22,8),(23,8),(24,22),(25,22),(25,23),(26,22),(26,23)],27)
 => ? = 1
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [2,1,4,6,5,3] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
 => ? = 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,6),(3,7),(3,9),(3,11),(4,6),(4,7),(4,8),(4,10),(6,14),(6,19),(7,13),(7,15),(7,19),(8,13),(8,19),(9,13),(9,16),(9,19),(10,14),(10,15),(10,19),(11,14),(11,15),(11,16),(12,16),(12,19),(13,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,5),(18,5),(19,17),(19,18)],20)
 => ? = 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,21),(1,22),(2,11),(2,13),(2,18),(3,12),(3,14),(3,18),(4,8),(4,9),(4,13),(4,18),(5,8),(5,10),(5,14),(5,18),(6,9),(6,10),(6,11),(6,12),(8,17),(8,19),(9,15),(9,19),(9,20),(10,1),(10,16),(10,19),(10,20),(11,15),(11,20),(12,16),(12,20),(13,15),(13,19),(14,16),(14,17),(15,21),(16,21),(16,22),(17,22),(18,17),(18,19),(18,20),(19,21),(19,22),(20,21),(20,22),(21,7),(22,7)],23)
 => ? = 2
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [2,1,6,5,4,3] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
 => ? = 2
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
 => ? = 4
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [3,2,4,5,1,6] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,17),(2,7),(2,13),(3,9),(3,11),(3,13),(4,1),(4,8),(4,11),(4,13),(5,7),(5,8),(5,9),(7,16),(8,12),(8,16),(8,17),(9,12),(9,16),(10,14),(11,10),(11,12),(11,17),(12,14),(12,15),(13,16),(13,17),(14,6),(15,6),(16,15),(17,14),(17,15)],18)
 => ? = 3
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,6,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,5,6,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,4,3,5,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,4,5,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,5,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,5,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,1,4,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,2,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,4,1,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,4,2,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,6,4,1,5,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
Description
The number of rowmotion orbits of a poset. Rowmotion is an operation on order ideals in a poset $P$. It sends an order ideal $I$ to the order ideal generated by the minimal antichain of $P \setminus I$.
Matching statistic: St001632
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001632: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 12%
Values
[2,1,3,4] => [2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 2
[2,3,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
 => 1
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 2
[1,3,4,2,5] => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[2,1,3,4,5] => [2,1,3,4,5] => [3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 3
[2,1,3,5,4] => [2,1,3,5,4] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2
[2,1,4,3,5] => [2,1,4,3,5] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => ? = 1
[2,1,5,3,4] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2
[2,1,5,4,3] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2
[2,3,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[2,3,1,5,4] => [3,2,1,5,4] => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1
[2,3,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[2,3,5,1,4] => [4,2,5,1,3] => [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1
[2,3,5,4,1] => [5,2,4,3,1] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1
[2,4,1,3,5] => [3,4,1,2,5] => [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 1
[2,4,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[2,4,5,1,3] => [4,5,3,1,2] => [5,1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2
[2,4,5,3,1] => [5,4,3,2,1] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 2
[3,1,2,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[3,1,4,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[3,2,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2
[3,2,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,1,2,3,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,1,3,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1
[4,2,1,3,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,2,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,3,1,2,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[4,3,2,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 2
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
 => ? = 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 3
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 2
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(1,10),(1,15),(2,8),(2,11),(2,15),(3,7),(3,8),(3,9),(4,7),(4,10),(4,11),(4,15),(5,17),(7,12),(7,13),(7,16),(8,13),(8,16),(9,12),(9,16),(10,12),(10,14),(11,5),(11,13),(11,14),(12,18),(13,17),(13,18),(14,17),(14,18),(15,5),(15,14),(15,16),(16,17),(16,18),(17,6),(18,6)],19)
 => ? = 1
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,12),(1,18),(1,20),(2,11),(2,13),(2,17),(2,18),(3,14),(3,15),(3,17),(3,18),(3,20),(4,9),(4,13),(4,15),(4,20),(5,7),(5,9),(5,12),(5,17),(6,7),(6,10),(6,11),(6,14),(6,20),(7,24),(7,25),(7,26),(9,19),(9,26),(10,24),(10,25),(11,21),(11,24),(11,25),(12,24),(12,26),(13,19),(13,21),(14,16),(14,24),(14,25),(15,16),(15,19),(15,21),(16,22),(16,23),(17,19),(17,25),(17,26),(18,21),(18,24),(18,26),(19,23),(20,16),(20,21),(20,25),(20,26),(21,22),(21,23),(22,8),(23,8),(24,22),(25,22),(25,23),(26,22),(26,23)],27)
 => ? = 1
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [2,1,4,6,5,3] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
 => ? = 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,6),(3,7),(3,9),(3,11),(4,6),(4,7),(4,8),(4,10),(6,14),(6,19),(7,13),(7,15),(7,19),(8,13),(8,19),(9,13),(9,16),(9,19),(10,14),(10,15),(10,19),(11,14),(11,15),(11,16),(12,16),(12,19),(13,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,5),(18,5),(19,17),(19,18)],20)
 => ? = 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,21),(1,22),(2,11),(2,13),(2,18),(3,12),(3,14),(3,18),(4,8),(4,9),(4,13),(4,18),(5,8),(5,10),(5,14),(5,18),(6,9),(6,10),(6,11),(6,12),(8,17),(8,19),(9,15),(9,19),(9,20),(10,1),(10,16),(10,19),(10,20),(11,15),(11,20),(12,16),(12,20),(13,15),(13,19),(14,16),(14,17),(15,21),(16,21),(16,22),(17,22),(18,17),(18,19),(18,20),(19,21),(19,22),(20,21),(20,22),(21,7),(22,7)],23)
 => ? = 2
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [2,1,6,5,4,3] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
 => ? = 2
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
 => ? = 4
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [3,2,4,5,1,6] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,17),(2,7),(2,13),(3,9),(3,11),(3,13),(4,1),(4,8),(4,11),(4,13),(5,7),(5,8),(5,9),(7,16),(8,12),(8,16),(8,17),(9,12),(9,16),(10,14),(11,10),(11,12),(11,17),(12,14),(12,15),(13,16),(13,17),(14,6),(15,6),(16,15),(17,14),(17,15)],18)
 => ? = 3
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 1
[2,5,6,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,5,6,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,4,3,5,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,4,5,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,5,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[2,6,5,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,1,4,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,2,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,4,1,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,5,6,4,2,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
[3,6,4,1,5,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 1
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
Matching statistic: St001633
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St001633: Posets ⟶ ℤResult quality: 6% ●values known / values provided: 6%●distinct values known / distinct values provided: 12%
Values
[2,1,3,4] => [2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)
 => ? = 2 - 1
[2,3,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[1,3,2,4,5] => [1,3,2,4,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => ? = 2 - 1
[1,3,4,2,5] => [1,4,3,2,5] => [2,5,4,3,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[2,1,3,4,5] => [2,1,3,4,5] => [3,2,4,5,1] => ([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => ? = 3 - 1
[2,1,3,5,4] => [2,1,3,5,4] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2 - 1
[2,1,4,3,5] => [2,1,4,3,5] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => ? = 1 - 1
[2,1,5,3,4] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2 - 1
[2,1,5,4,3] => [2,1,5,4,3] => [3,2,1,5,4] => ([(0,3),(0,4),(1,8),(2,7),(2,8),(3,1),(3,5),(4,2),(4,5),(5,7),(5,8),(7,6),(8,6)],9)
 => ? = 2 - 1
[2,3,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2 - 1
[2,3,1,5,4] => [3,2,1,5,4] => [4,3,2,1,5] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 1 - 1
[2,3,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[2,3,5,1,4] => [4,2,5,1,3] => [5,3,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1 - 1
[2,3,5,4,1] => [5,2,4,3,1] => [1,3,5,4,2] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 1 - 1
[2,4,1,3,5] => [3,4,1,2,5] => [4,5,2,3,1] => ([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => ? = 1 - 1
[2,4,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[2,4,5,1,3] => [4,5,3,1,2] => [5,1,4,2,3] => ([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => ? = 2 - 1
[2,4,5,3,1] => [5,4,3,2,1] => [1,5,4,3,2] => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 2 - 1
[3,1,2,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2 - 1
[3,1,4,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[3,2,1,4,5] => [3,2,1,4,5] => [4,3,2,5,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 2 - 1
[3,2,4,1,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[4,1,2,3,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[4,1,3,2,5] => [4,2,3,1,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => ? = 1 - 1
[4,2,1,3,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[4,2,3,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[4,3,1,2,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[4,3,2,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[1,2,4,3,5,6] => [1,2,4,3,5,6] => [2,3,5,4,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 2 - 1
[1,2,4,5,3,6] => [1,2,5,4,3,6] => [2,3,6,5,4,1] => ([(0,3),(0,4),(0,5),(1,13),(2,6),(2,8),(3,9),(3,10),(4,2),(4,10),(4,11),(5,1),(5,9),(5,11),(6,14),(6,15),(8,14),(9,12),(9,13),(10,8),(10,12),(11,6),(11,12),(11,13),(12,14),(12,15),(13,15),(14,7),(15,7)],16)
 => ? = 1 - 1
[1,3,2,4,5,6] => [1,3,2,4,5,6] => [2,4,3,5,6,1] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 3 - 1
[1,3,2,4,6,5] => [1,3,2,4,6,5] => [2,4,3,5,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 2 - 1
[1,3,2,5,4,6] => [1,3,2,5,4,6] => [2,4,3,6,5,1] => ([(0,1),(0,2),(0,3),(0,4),(1,9),(1,10),(1,15),(2,8),(2,11),(2,15),(3,7),(3,8),(3,9),(4,7),(4,10),(4,11),(4,15),(5,17),(7,12),(7,13),(7,16),(8,13),(8,16),(9,12),(9,16),(10,12),(10,14),(11,5),(11,13),(11,14),(12,18),(13,17),(13,18),(14,17),(14,18),(15,5),(15,14),(15,16),(16,17),(16,18),(17,6),(18,6)],19)
 => ? = 1 - 1
[1,3,2,6,4,5] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2 - 1
[1,3,2,6,5,4] => [1,3,2,6,5,4] => [2,4,3,1,6,5] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,14),(2,6),(2,8),(2,15),(3,10),(3,12),(3,14),(4,9),(4,10),(4,14),(5,2),(5,9),(5,11),(5,12),(6,17),(6,18),(8,17),(9,13),(9,15),(9,16),(10,13),(10,15),(11,8),(11,16),(12,6),(12,13),(12,16),(13,18),(14,15),(14,16),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7)],19)
 => ? = 2 - 1
[1,3,4,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2 - 1
[1,3,4,2,6,5] => [1,4,3,2,6,5] => [2,5,4,3,1,6] => ([(0,1),(0,3),(0,4),(0,5),(1,6),(1,15),(2,7),(2,8),(2,13),(3,10),(3,12),(3,15),(4,2),(4,11),(4,12),(4,15),(5,6),(5,10),(5,11),(6,16),(7,17),(8,17),(8,18),(10,14),(10,16),(11,8),(11,14),(11,16),(12,7),(12,13),(12,14),(13,17),(13,18),(14,17),(14,18),(15,13),(15,16),(16,18),(17,9),(18,9)],19)
 => ? = 1 - 1
[1,3,4,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1 - 1
[1,3,4,6,2,5] => [1,5,3,6,2,4] => [2,6,4,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(1,12),(1,18),(1,20),(2,11),(2,13),(2,17),(2,18),(3,14),(3,15),(3,17),(3,18),(3,20),(4,9),(4,13),(4,15),(4,20),(5,7),(5,9),(5,12),(5,17),(6,7),(6,10),(6,11),(6,14),(6,20),(7,24),(7,25),(7,26),(9,19),(9,26),(10,24),(10,25),(11,21),(11,24),(11,25),(12,24),(12,26),(13,19),(13,21),(14,16),(14,24),(14,25),(15,16),(15,19),(15,21),(16,22),(16,23),(17,19),(17,25),(17,26),(18,21),(18,24),(18,26),(19,23),(20,16),(20,21),(20,25),(20,26),(21,22),(21,23),(22,8),(23,8),(24,22),(25,22),(25,23),(26,22),(26,23)],27)
 => ? = 1 - 1
[1,3,4,6,5,2] => [1,6,3,5,4,2] => [2,1,4,6,5,3] => ([(0,1),(0,3),(0,4),(0,5),(1,11),(1,15),(2,6),(2,8),(2,18),(3,12),(3,13),(3,15),(4,10),(4,13),(4,15),(5,2),(5,10),(5,11),(5,12),(6,16),(6,17),(7,16),(7,17),(8,16),(10,14),(10,18),(11,8),(11,18),(12,6),(12,14),(12,18),(13,7),(13,14),(14,17),(15,7),(15,18),(16,9),(17,9),(18,16),(18,17)],19)
 => ? = 1 - 1
[1,3,5,2,4,6] => [1,4,5,2,3,6] => [2,5,6,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,10),(1,11),(1,12),(2,8),(2,9),(2,12),(3,6),(3,7),(3,9),(3,11),(4,6),(4,7),(4,8),(4,10),(6,14),(6,19),(7,13),(7,15),(7,19),(8,13),(8,19),(9,13),(9,16),(9,19),(10,14),(10,15),(10,19),(11,14),(11,15),(11,16),(12,16),(12,19),(13,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,5),(18,5),(19,17),(19,18)],20)
 => ? = 1 - 1
[1,3,5,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1 - 1
[1,3,5,6,2,4] => [1,5,6,4,2,3] => [2,6,1,5,3,4] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,21),(1,22),(2,11),(2,13),(2,18),(3,12),(3,14),(3,18),(4,8),(4,9),(4,13),(4,18),(5,8),(5,10),(5,14),(5,18),(6,9),(6,10),(6,11),(6,12),(8,17),(8,19),(9,15),(9,19),(9,20),(10,1),(10,16),(10,19),(10,20),(11,15),(11,20),(12,16),(12,20),(13,15),(13,19),(14,16),(14,17),(15,21),(16,21),(16,22),(17,22),(18,17),(18,19),(18,20),(19,21),(19,22),(20,21),(20,22),(21,7),(22,7)],23)
 => ? = 2 - 1
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [2,1,6,5,4,3] => ([(0,4),(0,5),(1,7),(2,9),(2,11),(3,2),(3,10),(4,3),(4,6),(5,1),(5,6),(6,7),(6,10),(7,11),(9,8),(10,9),(10,11),(11,8)],12)
 => ? = 2 - 1
[1,4,2,3,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2 - 1
[1,4,2,5,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1 - 1
[1,4,3,2,5,6] => [1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,16),(2,8),(2,10),(2,12),(3,8),(3,9),(3,11),(4,9),(4,10),(4,13),(5,1),(5,11),(5,12),(5,13),(6,17),(8,19),(9,14),(9,19),(10,15),(10,19),(11,14),(11,16),(11,19),(12,15),(12,16),(12,19),(13,6),(13,14),(13,15),(14,17),(14,18),(15,17),(15,18),(16,17),(16,18),(17,7),(18,7),(19,18)],20)
 => ? = 2 - 1
[1,4,3,5,2,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1 - 1
[1,5,2,3,4,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1 - 1
[1,5,2,4,3,6] => [1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,12),(1,15),(2,10),(2,12),(2,16),(3,11),(3,13),(3,15),(3,16),(4,8),(4,10),(4,11),(4,15),(5,8),(5,9),(5,13),(5,16),(6,18),(6,19),(8,14),(8,17),(8,20),(9,17),(9,21),(10,20),(10,21),(11,14),(11,20),(12,21),(13,6),(13,14),(13,17),(14,19),(15,17),(15,20),(15,21),(16,6),(16,20),(16,21),(17,18),(17,19),(18,7),(19,7),(20,18),(20,19),(21,18)],22)
 => ? = 1 - 1
[1,5,3,2,4,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1 - 1
[1,5,3,4,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1 - 1
[1,5,4,2,3,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1 - 1
[1,5,4,3,2,6] => [1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,2),(0,3),(0,5),(1,8),(1,12),(2,10),(3,6),(3,10),(4,1),(4,9),(4,11),(5,4),(5,6),(5,10),(6,9),(6,11),(8,7),(9,8),(9,12),(10,11),(11,12),(12,7)],13)
 => ? = 1 - 1
[2,1,3,4,5,6] => [2,1,3,4,5,6] => [3,2,4,5,6,1] => ([(0,3),(0,4),(0,5),(1,14),(2,1),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(6,14),(7,13),(7,14),(9,12),(10,6),(10,12),(11,7),(11,12),(12,13),(13,8),(14,8)],15)
 => ? = 4 - 1
[2,1,3,4,6,5] => [2,1,3,4,6,5] => [3,2,4,5,1,6] => ([(0,2),(0,3),(0,4),(0,5),(1,10),(1,17),(2,7),(2,13),(3,9),(3,11),(3,13),(4,1),(4,8),(4,11),(4,13),(5,7),(5,8),(5,9),(7,16),(8,12),(8,16),(8,17),(9,12),(9,16),(10,14),(11,10),(11,12),(11,17),(12,14),(12,15),(13,16),(13,17),(14,6),(15,6),(16,15),(17,14),(17,15)],18)
 => ? = 3 - 1
[2,4,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,5,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,5,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,5,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,5,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,5,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,5,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,2,5,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,2,5,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,3,5,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,3,5,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,5,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,5,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,5,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,5,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,5,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,5,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,2,3,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,2,3,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,2,4,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,2,4,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,3,1,2,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,3,1,4,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,3,2,1,4,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,3,2,4,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,3,4,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,3,4,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,4,1,2,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,4,1,3,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,4,2,1,3,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,4,2,3,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,4,3,1,2,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,5,6,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[2,5,6,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[2,6,4,3,5,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[2,6,4,5,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[2,6,5,3,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[2,6,5,4,3,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[3,5,6,1,4,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[3,5,6,2,4,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[3,5,6,4,1,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[3,5,6,4,2,1,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
[3,6,4,1,5,2,7] => [6,5,4,3,2,1,7] => [7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 0 = 1 - 1
Description
The number of simple modules with projective dimension two in the incidence algebra of the poset.
Matching statistic: St001232
(load all 4 compositions to match this statistic)
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%
Values
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 4
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 4
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 + 4
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 + 4
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ? = 1 + 4
[4,1,7,2,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,2,3,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,2,5,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,2,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,2,6,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,2,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,3,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,3,2,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,3,5,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,3,5,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,3,6,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,3,6,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,5,2,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,5,2,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,5,3,2,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,5,3,6,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,5,6,2,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,5,6,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,6,2,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,6,2,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,6,3,2,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,6,3,5,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,6,5,2,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,1,7,6,5,3,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,1,3,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,1,3,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,1,5,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,1,5,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,1,6,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,1,6,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,3,1,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,3,1,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,3,5,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,3,5,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,3,6,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,3,6,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,5,1,3,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,5,1,6,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,5,3,1,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,5,3,6,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,5,6,1,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,5,6,3,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,6,1,3,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,6,1,5,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,6,3,1,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,6,3,5,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,6,5,1,3] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,2,7,6,5,3,1] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,3,7,1,2,5,6] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
[4,3,7,1,2,6,5] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]
 => 6 = 2 + 4
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001876
Mapping
Mp00149: Permutations —Lehmer code rotation⟶ Permutations
Mp00208: Permutations —lattice of intervals⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%
Values
[2,1,3,4] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => ([(0,1)],2)
 => ? = 2
[2,3,1,4] => [3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => ([(0,1)],2)
 => ? = 1
[1,3,2,4,5] => [2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,9),(4,8),(5,7),(6,8),(6,9),(8,10),(9,10),(10,7)],11)
 => ([(0,1)],2)
 => ? = 2
[1,3,4,2,5] => [2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 1
[2,1,3,4,5] => [3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(0,1)],2)
 => ? = 3
[2,1,3,5,4] => [3,2,4,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[2,1,4,3,5] => [3,2,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ([(0,1)],2)
 => ? = 1
[2,1,5,3,4] => [3,2,1,5,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,6),(4,6),(5,7),(5,8),(6,10),(7,9),(8,9),(9,10)],11)
 => ([],1)
 => ? = 2
[2,1,5,4,3] => [3,2,1,4,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ([(0,1)],2)
 => ? = 2
[2,3,1,4,5] => [3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[2,3,1,5,4] => [3,4,2,1,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,6),(3,7),(4,7),(5,6),(5,8),(6,10),(7,8),(8,10),(10,9)],11)
 => ([(0,1)],2)
 => ? = 1
[2,3,4,1,5] => [3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,9),(3,11),(4,9),(4,10),(5,8),(5,11),(7,8),(8,6),(9,7),(10,7),(11,6)],12)
 => ([(0,1)],2)
 => ? = 1
[2,3,5,1,4] => [3,4,1,5,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => ([],1)
 => ? = 1
[2,3,5,4,1] => [3,4,1,2,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,7),(4,6),(5,6),(6,9),(7,9),(9,8)],10)
 => ([(0,1)],2)
 => ? = 1
[2,4,1,3,5] => [3,5,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
 => ([(0,1)],2)
 => ? = 1
[2,4,3,1,5] => [3,5,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1)],2)
 => ? = 1
[2,4,5,1,3] => [3,5,1,4,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? = 2
[2,4,5,3,1] => [3,5,1,2,4] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => ([],1)
 => ? = 2
[3,1,2,4,5] => [4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,9),(5,7),(6,9),(8,7),(9,8)],10)
 => ([(0,1)],2)
 => ? = 2
[3,1,4,2,5] => [4,2,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
 => ([(0,1)],2)
 => ? = 1
[3,2,1,4,5] => [4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(10,8)],11)
 => ([(0,1)],2)
 => ? = 2
[3,2,4,1,5] => [4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,6),(3,7),(4,7),(5,6),(5,9),(6,10),(7,8),(8,9),(9,10)],11)
 => ([(0,1)],2)
 => ? = 1
[4,1,2,3,5] => [5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,8),(2,7),(3,10),(4,9),(5,9),(5,10),(7,6),(8,6),(9,11),(10,11),(11,7),(11,8)],12)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,1,3,2,5] => [5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,2,1,3,5] => [5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(4,7),(5,9),(6,9),(7,10),(8,10),(9,7),(9,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,2,3,1,5] => [5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,3,1,2,5] => [5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(2,12),(3,12),(4,9),(5,10),(5,11),(7,6),(8,6),(9,8),(10,7),(11,7),(11,8),(12,9),(12,11)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[4,3,2,1,5] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,12),(2,11),(3,11),(3,14),(4,12),(4,15),(5,14),(5,15),(7,9),(8,10),(9,6),(10,6),(11,7),(12,8),(13,9),(13,10),(14,7),(14,13),(15,8),(15,13)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[1,2,4,3,5,6] => [2,3,5,4,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(2,14),(3,14),(4,11),(5,7),(6,12),(6,13),(8,10),(9,10),(10,7),(11,9),(12,8),(13,8),(13,9),(14,11),(14,13)],15)
 => ([(0,1)],2)
 => ? = 2
[1,2,4,5,3,6] => [2,3,5,6,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,10),(5,11),(6,7),(6,9),(7,12),(8,11),(9,12),(11,9),(12,10)],13)
 => ([(0,1)],2)
 => ? = 1
[1,3,2,4,5,6] => [2,4,3,5,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,12),(2,14),(3,14),(4,11),(5,7),(6,12),(6,13),(8,10),(9,10),(10,7),(11,9),(12,8),(13,8),(13,9),(14,11),(14,13)],15)
 => ([(0,1)],2)
 => ? = 3
[1,3,2,4,6,5] => [2,4,3,5,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,10),(4,9),(5,8),(6,11),(7,9),(7,10),(9,12),(10,12),(11,8),(12,11)],13)
 => ([(0,1)],2)
 => ? = 2
[1,3,2,5,4,6] => [2,4,3,6,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,10),(3,7),(4,7),(5,8),(6,8),(7,11),(8,9),(8,11),(9,12),(11,12),(12,10)],13)
 => ([(0,1)],2)
 => ? = 1
[1,3,2,6,4,5] => [2,4,3,1,6,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,7),(4,7),(5,8),(6,8),(7,11),(8,9),(9,10),(10,11)],12)
 => ([],1)
 => ? = 2
[1,3,2,6,5,4] => [2,4,3,1,5,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,10),(5,11),(6,7),(6,9),(7,12),(8,11),(9,12),(10,9),(11,10)],13)
 => ([(0,1)],2)
 => ? = 2
[1,3,4,2,5,6] => [2,4,5,3,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,10),(6,11),(7,11),(8,12),(9,12),(11,8),(11,9),(12,10)],13)
 => ([(0,1)],2)
 => ? = 2
[1,3,4,2,6,5] => [2,4,5,3,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
 => ([(0,1)],2)
 => ? = 1
[1,3,4,5,2,6] => [2,4,5,6,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(3,8),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13)
 => ([(0,1)],2)
 => ? = 1
[1,3,4,6,2,5] => [2,4,5,1,6,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,8)],9)
 => ([],1)
 => ? = 1
[1,3,4,6,5,2] => [2,4,5,1,3,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,9),(3,9),(4,7),(5,7),(6,8),(7,9),(9,8)],10)
 => ([(0,1)],2)
 => ? = 1
[1,3,5,2,4,6] => [2,4,6,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(9,7)],10)
 => ([(0,1)],2)
 => ? = 1
[1,3,5,4,2,6] => [2,4,6,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
 => ([(0,1)],2)
 => ? = 1
[1,3,5,6,2,4] => [2,4,6,1,5,3] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 2
[1,3,5,6,4,2] => [2,4,6,1,3,5] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 2
[1,4,2,3,5,6] => [2,5,3,4,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,10),(6,11),(7,11),(8,12),(9,12),(11,8),(11,9),(12,10)],13)
 => ([(0,1)],2)
 => ? = 2
[1,4,2,5,3,6] => [2,5,3,6,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,9),(6,7),(7,8),(9,7)],10)
 => ([(0,1)],2)
 => ? = 1
[1,4,3,2,5,6] => [2,5,4,3,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,7),(6,11),(6,12),(8,7),(9,8),(10,8),(11,13),(12,13),(13,9),(13,10)],14)
 => ([(0,1)],2)
 => ? = 2
[1,4,3,5,2,6] => [2,5,4,6,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
 => ([(0,1)],2)
 => ? = 1
[1,5,2,3,4,6] => [2,6,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,7),(3,7),(3,8),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13)
 => ([(0,1)],2)
 => ? = 1
[1,5,2,4,3,6] => [2,6,3,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
 => ([(0,1)],2)
 => ? = 1
[1,5,3,2,4,6] => [2,6,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,10),(5,11),(6,8),(7,11),(9,10),(10,8),(11,9)],12)
 => ([(0,1)],2)
 => ? = 1
[1,5,3,4,2,6] => [2,6,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,10),(4,9),(5,8),(6,11),(7,9),(7,10),(9,12),(10,12),(11,8),(12,11)],13)
 => ([(0,1)],2)
 => ? = 1
[1,5,4,2,3,6] => [2,6,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,9),(5,11),(6,7),(6,10),(7,12),(8,10),(10,12),(11,9),(12,11)],13)
 => ([(0,1)],2)
 => ? = 1
[1,5,4,3,2,6] => [2,6,5,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,13),(3,12),(4,7),(5,12),(5,14),(6,13),(6,14),(8,11),(9,8),(10,8),(11,7),(12,9),(13,10),(14,9),(14,10)],15)
 => ([(0,1)],2)
 => ? = 1
[2,1,3,4,5,6] => [3,2,4,5,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,13),(3,12),(4,7),(5,11),(5,14),(6,12),(6,14),(8,10),(9,10),(10,7),(11,8),(12,9),(13,11),(14,8),(14,9)],15)
 => ([(0,1)],2)
 => ? = 4
[2,1,3,4,6,5] => [3,2,4,5,1,6] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,8),(2,8),(3,7),(4,9),(5,11),(6,7),(6,10),(7,12),(8,10),(10,12),(11,9),(12,11)],13)
 => ([(0,1)],2)
 => ? = 3
[5,1,2,3,4,6] => [6,2,3,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,12),(5,12),(5,15),(6,13),(6,15),(8,14),(9,14),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,9)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,1,2,4,3,6] => [6,2,3,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,1,3,2,4,6] => [6,2,4,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,9),(2,8),(3,11),(4,10),(5,13),(6,13),(8,12),(9,12),(10,7),(11,7),(12,10),(12,11),(13,8),(13,9)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,1,3,4,2,6] => [6,2,4,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,1,4,2,3,6] => [6,2,5,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,1,4,3,2,6] => [6,2,5,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,2,1,3,4,6] => [6,3,2,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,11),(4,12),(5,12),(6,8),(6,11),(8,13),(9,7),(10,7),(11,13),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,2,1,4,3,6] => [6,3,2,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,8),(4,8),(5,7),(6,7),(7,11),(8,11),(9,12),(10,12),(11,9),(11,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,2,3,1,4,6] => [6,3,4,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,2,3,4,1,6] => [6,3,4,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,2,4,1,3,6] => [6,3,5,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,2,4,3,1,6] => [6,3,5,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,3,1,2,4,6] => [6,4,2,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,7),(2,7),(3,9),(4,8),(5,11),(6,10),(7,10),(8,12),(9,12),(10,11),(11,8),(11,9)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,3,1,4,2,6] => [6,4,2,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,10),(3,10),(4,10),(5,8),(6,7),(7,9),(8,9),(10,7),(10,8)],11)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,3,2,1,4,6] => [6,4,3,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,10),(2,9),(3,12),(4,11),(5,13),(6,11),(6,12),(8,13),(9,7),(10,7),(11,8),(12,8),(13,9),(13,10)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,3,2,4,1,6] => [6,4,3,5,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,3,4,1,2,6] => [6,4,5,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,10),(3,13),(4,13),(5,14),(6,14),(8,7),(9,7),(10,8),(11,9),(12,8),(12,9),(13,10),(13,12),(14,11),(14,12)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,3,4,2,1,6] => [6,4,5,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,4,1,2,3,6] => [6,5,2,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,12),(3,11),(4,10),(5,12),(5,13),(6,11),(6,15),(8,7),(9,7),(10,9),(11,8),(12,14),(13,14),(14,10),(14,15),(15,8),(15,9)],16)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,4,1,3,2,6] => [6,5,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,4,2,1,3,6] => [6,5,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,11),(2,14),(3,12),(4,12),(5,10),(6,11),(6,13),(8,7),(9,7),(10,9),(11,8),(12,14),(13,8),(13,9),(14,10),(14,13)],15)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,4,2,3,1,6] => [6,5,3,4,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,17),(2,17),(3,13),(4,12),(5,12),(5,15),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,8),(13,9),(14,10),(14,11),(15,8),(15,14),(16,9),(16,14),(17,15),(17,16)],18)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[5,4,3,1,2,6] => [6,5,4,2,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,13),(2,17),(3,17),(4,12),(5,15),(5,16),(6,13),(6,16),(8,10),(9,11),(10,7),(11,7),(12,9),(13,8),(14,10),(14,11),(15,9),(15,14),(16,8),(16,14),(17,12),(17,15)],18)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,5,4,6,2,1,3,8] => [8,6,5,7,3,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,14),(3,15),(4,15),(5,13),(6,12),(7,17),(8,18),(10,9),(11,9),(12,10),(13,11),(14,17),(15,18),(16,10),(16,11),(17,12),(17,16),(18,13),(18,16)],19)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,3,6,2,5,1,4,8] => [8,4,7,3,6,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,5,3,2,6,1,4,8] => [8,6,4,3,7,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,13),(3,13),(4,13),(5,11),(6,10),(7,9),(8,9),(9,13),(10,12),(11,12),(13,10),(13,11)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,2,1,4,3,6,5,8] => [8,3,2,5,4,7,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,17),(2,17),(3,14),(4,14),(5,15),(6,15),(7,13),(8,12),(10,16),(11,16),(12,9),(13,9),(14,11),(15,10),(16,12),(16,13),(17,10),(17,11)],18)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,3,4,1,2,6,5,8] => [8,4,5,2,3,7,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,15),(10,14),(11,14),(12,16),(13,16),(14,15),(15,12),(15,13)],17)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,4,3,2,1,6,5,8] => [8,5,4,3,2,7,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,13),(3,16),(4,15),(5,17),(6,17),(7,15),(7,19),(8,16),(8,19),(10,12),(11,12),(12,18),(13,9),(14,9),(15,10),(16,11),(17,18),(18,13),(18,14),(19,10),(19,11)],20)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,3,5,1,6,2,4,8] => [8,4,6,2,7,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,2,1,5,6,3,4,8] => [8,3,2,6,7,4,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,12),(3,11),(4,11),(5,10),(6,10),(7,9),(8,9),(9,15),(10,14),(11,14),(12,16),(13,16),(14,15),(15,12),(15,13)],17)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,2,1,6,5,4,3,8] => [8,3,2,7,6,5,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,13),(3,16),(4,15),(5,17),(6,17),(7,15),(7,19),(8,16),(8,19),(10,12),(11,12),(12,18),(13,9),(14,9),(15,10),(16,11),(17,18),(18,13),(18,14),(19,10),(19,11)],20)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,3,6,1,5,4,2,8] => [8,4,7,2,6,5,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,13),(3,13),(4,13),(5,11),(6,10),(7,9),(8,9),(9,13),(10,12),(11,12),(13,10),(13,11)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,4,6,5,1,3,2,8] => [8,5,7,6,2,4,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,14),(2,14),(3,15),(4,15),(5,13),(6,12),(7,17),(8,18),(10,9),(11,9),(12,10),(13,11),(14,17),(15,18),(16,10),(16,11),(17,12),(17,16),(18,13),(18,16)],19)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,4,6,3,1,5,2,8] => [8,5,7,4,2,6,3,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,4,6,1,5,2,3,8] => [8,5,7,2,6,3,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,13),(2,13),(3,13),(4,13),(5,11),(6,10),(7,9),(8,9),(9,13),(10,12),(11,12),(13,10),(13,11)],14)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,3,6,1,5,2,4,8] => [8,4,7,2,6,3,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,5,2,6,4,1,3,8] => [8,6,3,7,5,2,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,4,2,6,1,5,3,8] => [8,5,3,7,2,6,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,4,2,5,1,6,3,8] => [8,5,3,6,2,7,4,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,3,1,4,6,2,5,8] => [8,4,2,5,7,3,6,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,2,6,3,5,1,4,8] => [8,3,7,4,6,2,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[7,2,5,1,3,6,4,8] => [8,3,6,2,4,7,5,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,12),(2,12),(3,12),(4,12),(5,12),(6,12),(7,10),(8,9),(9,11),(10,11),(12,9),(12,10)],13)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Matching statistic: St001964
(load all 2 compositions to match this statistic)
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00232: Dyck paths —parallelogram poset⟶ Posets
St001964: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 25%
Values
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 1 = 2 - 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0]
 => ([(0,3),(2,1),(3,2)],4)
 => 0 = 1 - 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 2 - 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 3 - 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ? = 2 - 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ? = 2 - 1
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ? = 2 - 1
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 2 - 1
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 - 1
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 - 1
[3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 - 1
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ? = 2 - 1
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,0]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0 = 1 - 1
[4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[4,1,3,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[4,2,1,3,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[4,3,1,2,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ? = 1 - 1
[1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 2 - 1
[1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,0,1,0,1,1,0,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ? = 1 - 1
[1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 3 - 1
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ? = 2 - 1
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ? = 2 - 1
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ? = 2 - 1
[1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ? = 2 - 1
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[1,3,4,6,2,5] => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ? = 1 - 1
[1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,0,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ? = 1 - 1
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2 - 1
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ? = 2 - 1
[1,4,2,3,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ? = 2 - 1
[1,4,2,5,3,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ? = 1 - 1
[1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ? = 2 - 1
[1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ? = 1 - 1
[1,5,2,3,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 1 - 1
[1,5,2,4,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 1 - 1
[1,5,3,2,4,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 1 - 1
[1,5,3,4,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 1 - 1
[1,5,4,2,3,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 1 - 1
[1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => ([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8)
 => ? = 1 - 1
[2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => ([(0,5),(1,8),(2,7),(3,2),(3,6),(4,1),(4,6),(5,3),(5,4),(6,7),(6,8),(7,9),(8,9)],10)
 => ? = 4 - 1
[2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 3 - 1
[2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 1 - 1
[2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 2 - 1
[2,1,3,6,4,5] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 3 - 1
[2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ? = 3 - 1
[2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ? = 2 - 1
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ? = 1 - 1
[2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 2 - 1
[2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => ([(0,5),(1,7),(2,7),(3,6),(4,6),(5,1),(5,2),(7,3),(7,4)],8)
 => ? = 1 - 1
[2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ? = 2 - 1
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,6,1,5,4] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,6,4,1,5] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,1,4,5,2,6] => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [1,1,0,1,0,0,1,1,0,0,1,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,1,2,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,1,3,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,2,1,5,3,6] => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,2,3,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,3,1,5,2,6] => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
[4,3,2,5,1,6] => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,0]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 0 = 1 - 1
Description
The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
Matching statistic: St000454
Mapping
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
St000454: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%
Values
[2,1,3,4] => [2,1,4,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[2,3,1,4] => [2,4,1,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[1,3,2,4,5] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[1,3,4,2,5] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,1,3,4,5] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3 + 1
[2,1,3,5,4] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[2,1,4,3,5] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,1,5,3,4] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[2,1,5,4,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[2,3,1,4,5] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[2,3,1,5,4] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,3,4,1,5] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,3,5,1,4] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,3,5,4,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,4,1,3,5] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,4,3,1,5] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[2,4,5,1,3] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[2,4,5,3,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[3,1,2,4,5] => [3,1,5,4,2] => [[.,[.,.]],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[3,1,4,2,5] => [3,1,5,4,2] => [[.,[.,.]],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[3,2,1,4,5] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 1
[3,2,4,1,5] => [3,2,5,1,4] => [[[.,.],.],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[4,1,2,3,5] => [4,1,5,3,2] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[4,1,3,2,5] => [4,1,5,3,2] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[4,2,1,3,5] => [4,2,1,5,3] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 1
[4,2,3,1,5] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 1
[4,3,1,2,5] => [4,3,1,5,2] => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[4,3,2,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 1
[1,2,4,3,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,2,4,5,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,2,4,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3 + 1
[1,3,2,4,6,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,3,2,5,4,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,2,6,4,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,3,2,6,5,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,3,4,2,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,3,4,2,6,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,4,5,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,4,6,2,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,4,6,5,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,5,2,4,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,5,4,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,3,5,6,2,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,4,2,3,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,4,2,5,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,4,3,2,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 1
[1,4,3,5,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,5,2,3,4,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[1,5,2,4,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 1
[6,3,1,2,4,5,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,2,5,4,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,2,7,4,5] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,2,7,5,4] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,4,2,5,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,4,5,2,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,4,7,2,5] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,4,7,5,2] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,5,2,4,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,5,4,2,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,5,7,2,4] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,1,5,7,4,2] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,1,4,5,7] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,1,5,4,7] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,1,7,4,5] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,1,7,5,4] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,4,1,5,7] => [6,3,2,7,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,4,5,1,7] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,4,7,1,5] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,4,7,5,1] => [6,3,2,7,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,5,1,4,7] => [6,3,2,7,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,5,4,1,7] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,5,7,1,4] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,2,5,7,4,1] => [6,3,2,7,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,1,2,5,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,1,5,2,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,1,7,2,5] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,1,7,5,2] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,2,1,5,7] => [6,3,7,2,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,2,5,1,7] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,2,7,1,5] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,2,7,5,1] => [6,3,7,2,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,5,1,2,7] => [6,3,7,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,5,2,1,7] => [6,3,7,5,2,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,5,7,1,2] => [6,3,7,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,4,5,7,2,1] => [6,3,7,5,4,2,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,1,2,4,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,1,4,2,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,1,7,2,4] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,1,7,4,2] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,2,1,4,7] => [6,3,7,2,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,2,4,1,7] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,2,7,1,4] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,2,7,4,1] => [6,3,7,2,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,4,1,2,7] => [6,3,7,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,4,2,1,7] => [6,3,7,5,2,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,4,7,1,2] => [6,3,7,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
[6,3,5,4,7,2,1] => [6,3,7,5,4,2,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 2 = 1 + 1
Description
The largest eigenvalue of a graph if it is integral. If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree. This statistic is undefined if the largest eigenvalue of the graph is not integral.
Matching statistic: St000422
Mapping
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 12%
Values
[2,1,3,4] => [2,1,4,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 7
[2,3,1,4] => [2,4,1,3] => [[.,.],[[.,.],.]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 7
[1,3,2,4,5] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[1,3,4,2,5] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,1,3,4,5] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 3 + 7
[2,1,3,5,4] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[2,1,4,3,5] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,1,5,3,4] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[2,1,5,4,3] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[2,3,1,4,5] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[2,3,1,5,4] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,3,4,1,5] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,3,5,1,4] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,3,5,4,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,4,1,3,5] => [2,5,1,4,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,4,3,1,5] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[2,4,5,1,3] => [2,5,4,1,3] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[2,4,5,3,1] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[3,1,2,4,5] => [3,1,5,4,2] => [[.,[.,.]],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[3,1,4,2,5] => [3,1,5,4,2] => [[.,[.,.]],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[3,2,1,4,5] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 2 + 7
[3,2,4,1,5] => [3,2,5,1,4] => [[[.,.],.],[[.,.],.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[4,1,2,3,5] => [4,1,5,3,2] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[4,1,3,2,5] => [4,1,5,3,2] => [[.,[[.,.],.]],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[4,2,1,3,5] => [4,2,1,5,3] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 7
[4,2,3,1,5] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 7
[4,3,1,2,5] => [4,3,1,5,2] => [[[.,[.,.]],.],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[4,3,2,1,5] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ? = 1 + 7
[1,2,4,3,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,2,4,5,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,2,4,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 3 + 7
[1,3,2,4,6,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,3,2,5,4,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,2,6,4,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,3,2,6,5,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,3,4,2,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,3,4,2,6,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,4,5,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,4,6,2,5] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,4,6,5,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,5,2,4,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,5,4,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,3,5,6,2,4] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,3,5,6,4,2] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,4,2,3,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,4,2,5,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,4,3,2,5,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 2 + 7
[1,4,3,5,2,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,5,2,3,4,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[1,5,2,4,3,6] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => ? = 1 + 7
[6,3,1,2,4,5,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,2,5,4,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,2,7,4,5] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,2,7,5,4] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,4,2,5,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,4,5,2,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,4,7,2,5] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,4,7,5,2] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,5,2,4,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,5,4,2,7] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,5,7,2,4] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,1,5,7,4,2] => [6,3,1,7,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,1,4,5,7] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,1,5,4,7] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,1,7,4,5] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,1,7,5,4] => [6,3,2,1,7,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,4,1,5,7] => [6,3,2,7,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,4,5,1,7] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,4,7,1,5] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,4,7,5,1] => [6,3,2,7,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,5,1,4,7] => [6,3,2,7,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,5,4,1,7] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,5,7,1,4] => [6,3,2,7,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,2,5,7,4,1] => [6,3,2,7,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,1,2,5,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,1,5,2,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,1,7,2,5] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,1,7,5,2] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,2,1,5,7] => [6,3,7,2,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,2,5,1,7] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,2,7,1,5] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,2,7,5,1] => [6,3,7,2,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,5,1,2,7] => [6,3,7,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,5,2,1,7] => [6,3,7,5,2,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,5,7,1,2] => [6,3,7,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,4,5,7,2,1] => [6,3,7,5,4,2,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,1,2,4,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,1,4,2,7] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,1,7,2,4] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,1,7,4,2] => [6,3,7,1,5,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,2,1,4,7] => [6,3,7,2,1,5,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,2,4,1,7] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,2,7,1,4] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,2,7,4,1] => [6,3,7,2,5,4,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,4,1,2,7] => [6,3,7,5,1,4,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,4,2,1,7] => [6,3,7,5,2,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,4,7,1,2] => [6,3,7,5,4,1,2] => [[[.,[.,.]],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
[6,3,5,4,7,2,1] => [6,3,7,5,4,2,1] => [[[[.,.],.],[[.,.],.]],[.,.]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
 => 8 = 1 + 7
Description
The energy of a graph, if it is integral. The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3]. The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
The following 7 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000633The size of the automorphism group of a poset. St000640The rank of the largest boolean interval in a poset. St001399The distinguishing number of a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St000850The number of 1/2-balanced pairs in a poset. St001095The number of non-isomorphic posets with precisely one further covering relation. St001396Number of triples of incomparable elements in a finite poset.