Your data matches 31 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001568
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001568: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([(0,2),(2,1)],3)
 => [3]
 => [1,1,1]
 => [1,1]
 => 2
([(2,3)],4)
 => [2,1,1]
 => [2,2]
 => [2]
 => 1
([(1,2),(1,3)],4)
 => [2,1,1]
 => [2,2]
 => [2]
 => 1
([(0,1),(0,2),(0,3)],4)
 => [2,1,1]
 => [2,2]
 => [2]
 => 1
([(0,2),(0,3),(3,1)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 2
([(1,2),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 2
([(0,3),(3,1),(3,2)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 2
([(1,3),(2,3)],4)
 => [2,1,1]
 => [2,2]
 => [2]
 => 1
([(0,3),(1,3),(3,2)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [2,1,1]
 => [2,2]
 => [2]
 => 1
([(0,3),(2,1),(3,2)],4)
 => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [3,1]
 => [2,1,1]
 => [1,1]
 => 2
([],5)
 => [1,1,1,1,1]
 => [3,2]
 => [2]
 => 1
([(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,1]
 => 2
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,1]
 => 2
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,1]
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,1]
 => 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,1]
 => 2
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,1]
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,1]
 => 2
([(0,4),(1,4),(2,3)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(1,4),(2,3)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(1,4),(2,3),(2,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,4),(1,2),(1,3)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [2,2,1]
 => [2,2,1]
 => [2,1]
 => 1
([(1,4),(3,2),(4,3)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [5]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [4,1]
 => [2,1,1,1]
 => [1,1,1]
 => 2
([],6)
 => [1,1,1,1,1,1]
 => [3,2,1]
 => [2,1]
 => 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [4,2]
 => [2]
 => 1
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [4,2]
 => [2]
 => 1
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [4,2]
 => [2]
 => 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [4,2]
 => [2]
 => 1
Description
The smallest positive integer that does not appear twice in the partition.
Matching statistic: St001232
(load all 3 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 33%
Values
([(0,2),(2,1)],3)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(1,2),(1,3)],4)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 1 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 2 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
 => ? = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,1,0,0,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 2 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ?
 => ? = 1 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ?
 => ? = 1 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ?
 => ? = 1 - 2
([(2,3),(2,4),(2,5)],6)
 => [18,18,18,18,18,18,18,18,18,18]
 => ?
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(1,5)],6)
 => [24,24,24,24,24,24]
 => ?
 => ?
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [10,10,10,10]
 => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [24,24,24]
 => ?
 => ?
 => ? = 1 - 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [10,10,10,10]
 => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [48]
 => ?
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [18,18]
 => ?
 => ?
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,0,1,0]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => ? = 2 - 2
([(2,3),(2,4),(4,5)],6)
 => [18,18,18,18,18]
 => ?
 => ?
 => ? = 1 - 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => [48]
 => ?
 => ?
 => ? = 1 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6]
 => ?
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0]
 => ? = 2 - 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => ? = 2 - 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 2 - 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(1,5),(3,4),(4,2),(5,3)],6)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 2 - 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [1]
 => [1,0]
 => [1,0]
 => 0 = 2 - 2
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [3]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0 = 2 - 2
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)
 => [6]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)
 => [7]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0 = 2 - 2
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0 = 2 - 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0 = 2 - 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001487
(load all 2 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001487: Skew partitions ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 33%
Values
([(0,2),(2,1)],3)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 2 - 1
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [[5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [[15,5,5],[]]
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 1
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ? = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => [18,18,18,18,18,18,18,18,18,18]
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [24,24,24,24,24,24]
 => ?
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [24,24,24]
 => ?
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [48]
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [18,18]
 => ?
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [[8],[]]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [[5,5],[]]
 => ? = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [18,18,18,18,18]
 => ?
 => ? = 1 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [48]
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [[12],[]]
 => ? = 2 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [[6],[]]
 => ? = 2 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [[7],[]]
 => ? = 2 - 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 1 = 2 - 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
Description
The number of inner corners of a skew partition.
Matching statistic: St001490
(load all 3 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001490: Skew partitions ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 33%
Values
([(0,2),(2,1)],3)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 2 - 1
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [[5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [[15,5,5],[]]
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 1
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ? = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => [18,18,18,18,18,18,18,18,18,18]
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [24,24,24,24,24,24]
 => ?
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [24,24,24]
 => ?
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [48]
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [18,18]
 => ?
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [[8],[]]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [[5,5],[]]
 => ? = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [18,18,18,18,18]
 => ?
 => ? = 1 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [48]
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [[12],[]]
 => ? = 2 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [[6],[]]
 => ? = 2 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [[7],[]]
 => ? = 2 - 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 1 = 2 - 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [1]
 => [[1],[]]
 => 1 = 2 - 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [3]
 => [[3],[]]
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 1 = 2 - 1
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => 1 = 2 - 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [2]
 => [[2],[]]
 => 1 = 2 - 1
Description
The number of connected components of a skew partition.
Matching statistic: St001435
(load all 2 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001435: Skew partitions ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 33%
Values
([(0,2),(2,1)],3)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 1 - 2
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [[5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [[15,5,5],[]]
 => ? = 1 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => ? = 1 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ? = 1 - 2
([(2,3),(2,4),(2,5)],6)
 => [18,18,18,18,18,18,18,18,18,18]
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(1,5)],6)
 => [24,24,24,24,24,24]
 => ?
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 1 - 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [24,24,24]
 => ?
 => ? = 1 - 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [48]
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [18,18]
 => ?
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [[8],[]]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [[5,5],[]]
 => ? = 2 - 2
([(2,3),(2,4),(4,5)],6)
 => [18,18,18,18,18]
 => ?
 => ? = 1 - 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => [48]
 => ?
 => ? = 1 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [[12],[]]
 => ? = 2 - 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [[6],[]]
 => ? = 2 - 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [[7],[]]
 => ? = 2 - 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 0 = 2 - 2
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 0 = 2 - 2
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
Description
The number of missing boxes in the first row.
Matching statistic: St001438
(load all 2 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
St001438: Skew partitions ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 33%
Values
([(0,2),(2,1)],3)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(2,3)],4)
 => [4,4,4]
 => [[4,4,4],[]]
 => ? = 1 - 2
([(1,2),(1,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 2
([(0,2),(0,3),(3,1)],4)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(1,2),(2,3)],4)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,3),(3,1),(3,2)],4)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(1,3),(2,3)],4)
 => [8]
 => [[8],[]]
 => ? = 1 - 2
([(0,3),(1,3),(3,2)],4)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => [[3,3],[]]
 => ? = 1 - 2
([(0,3),(2,1),(3,2)],4)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(0,3),(1,2),(2,3)],4)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 2 - 2
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 2
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 2 - 2
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => [[15,15],[]]
 => ? = 2 - 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 2 - 2
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 2
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 2
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 2
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 2
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => [[5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => [[15,5,5],[]]
 => ? = 1 - 2
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => [[5,5,5,5],[]]
 => ? = 1 - 2
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => [[10,10],[]]
 => ? = 1 - 2
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => [[10,4,4],[]]
 => ? = 1 - 2
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => [[12,4],[]]
 => ? = 1 - 2
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => [[14],[]]
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => [[6,6],[]]
 => ? = 1 - 2
([(1,4),(3,2),(4,3)],5)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 2
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 2
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ?
 => ? = 1 - 2
([(2,3),(2,4),(2,5)],6)
 => [18,18,18,18,18,18,18,18,18,18]
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(1,5)],6)
 => [24,24,24,24,24,24]
 => ?
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => [[5,5,5,5,5,5,5,5,5,5,5,5],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => [[4,4,4,4,4,4],[]]
 => ? = 1 - 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [24,24,24]
 => ?
 => ? = 1 - 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [10,10,10,10]
 => [[10,10,10,10],[]]
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [48]
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [18,18]
 => ?
 => ? = 1 - 2
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => [[3,3],[]]
 => ? = 2 - 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => [[8],[]]
 => ? = 2 - 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => [[5,5],[]]
 => ? = 2 - 2
([(2,3),(2,4),(4,5)],6)
 => [18,18,18,18,18]
 => ?
 => ? = 1 - 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => [48]
 => ?
 => ? = 1 - 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => [[15,15],[]]
 => ? = 1 - 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6]
 => ?
 => ? = 1 - 2
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [12]
 => [[12],[]]
 => ? = 2 - 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [6]
 => [[6],[]]
 => ? = 2 - 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)
 => [7]
 => [[7],[]]
 => ? = 2 - 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 0 = 2 - 2
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => [3,2]
 => [[3,2],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
 => [4]
 => [[4],[]]
 => 0 = 2 - 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
 => [3,2]
 => [[3,2],[]]
 => 0 = 2 - 2
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [1]
 => [[1],[]]
 => 0 = 2 - 2
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [3]
 => [[3],[]]
 => 0 = 2 - 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
 => [2,2]
 => [[2,2],[]]
 => 0 = 2 - 2
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
 => [5]
 => [[5],[]]
 => 0 = 2 - 2
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [2]
 => [[2],[]]
 => 0 = 2 - 2
Description
The number of missing boxes of a skew partition.
Matching statistic: St001491
(load all 2 compositions to match this statistic)
Mapping
Mp00307: Posets —promotion cycle type⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 33%
Values
([(0,2),(2,1)],3)
 => [1]
 => 10 => 1 = 2 - 1
([(2,3)],4)
 => [4,4,4]
 => 1110000 => ? = 1 - 1
([(1,2),(1,3)],4)
 => [8]
 => 100000000 => ? = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => [3,3]
 => 11000 => ? = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [2]
 => 100 => 1 = 2 - 1
([(1,2),(2,3)],4)
 => [4]
 => 10000 => ? = 2 - 1
([(0,3),(3,1),(3,2)],4)
 => [2]
 => 100 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => [8]
 => 100000000 => ? = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => [2]
 => 100 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => [3,3]
 => 11000 => ? = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => [1]
 => 10 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [3]
 => 1000 => 1 = 2 - 1
([],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => 11111111111111111111111100000 => ? = 1 - 1
([(3,4)],5)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => 11111111111100000 => ? = 2 - 1
([(2,3),(2,4)],5)
 => [10,10,10,10]
 => 11110000000000 => ? = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [15,15]
 => 11000000000000000 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [4,4,4,4,4,4]
 => 1111110000 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [2]
 => 100 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [10,10,10,10]
 => 11110000000000 => ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [15,15]
 => 11000000000000000 => ? = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [4,4,4,4,4,4]
 => 1111110000 => ? = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => [10,10]
 => 110000000000 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [12,4]
 => 10000000010000 => ? = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [14]
 => 100000000000000 => ? = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [6,6]
 => 11000000 => ? = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [2]
 => 100 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => [10,4,4]
 => 1000000110000 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [5,5,5,5,5,5]
 => 11111100000 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => [15,5,5]
 => 100000000001100000 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [5,5,5,5]
 => 111100000 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => [10,10]
 => 110000000000 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [10,4,4]
 => 1000000110000 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [4]
 => 10000 => ? = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => [12,4]
 => 10000000010000 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [14]
 => 100000000000000 => ? = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [6,6]
 => 11000000 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => [5]
 => 100000 => ? = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [2]
 => 100 => 1 = 2 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [1]
 => 10 => 1 = 2 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [4]
 => 10000 => ? = 2 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [2]
 => 100 => 1 = 2 - 1
([],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ? => ? = 1 - 1
([(4,5)],6)
 => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
 => ? => ? = 1 - 1
([(3,4),(3,5)],6)
 => [12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12]
 => ? => ? = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => [18,18,18,18,18,18,18,18,18,18]
 => ? => ? = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [24,24,24,24,24,24]
 => ? => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]
 => 11111111111111111111111100000 => ? = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [5,5,5,5,5,5,5,5,5,5,5,5]
 => 11111111111100000 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [10,10,10,10]
 => 11110000000000 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [15,15]
 => 11000000000000000 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,4,4,4,4,4]
 => 1111110000 => ? = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [24,24,24]
 => ? => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [10,10,10,10]
 => 11110000000000 => ? = 1 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [48]
 => ? => ? = 1 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [18,18]
 => ? => ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [3,3]
 => 11000 => ? = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8]
 => 100000000 => ? = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,5]
 => 1100000 => ? = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [18,18,18,18,18]
 => ? => ? = 1 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [48]
 => ? => ? = 1 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [15,15]
 => 11000000000000000 => ? = 1 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
 => [2]
 => 100 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => [2]
 => 100 => 1 = 2 - 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
 => [2]
 => 100 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => [2]
 => 100 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => [1]
 => 10 => 1 = 2 - 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => [2]
 => 100 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => [2]
 => 100 => 1 = 2 - 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
 => [2]
 => 100 => 1 = 2 - 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => [2]
 => 100 => 1 = 2 - 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)
 => [2,2]
 => 1100 => 1 = 2 - 1
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)
 => [2]
 => 100 => 1 = 2 - 1
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)
 => [3]
 => 1000 => 1 = 2 - 1
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => [1]
 => 10 => 1 = 2 - 1
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
 => [3]
 => 1000 => 1 = 2 - 1
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let $A_n=K[x]/(x^n)$. We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Matching statistic: St001257
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001257: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 67%
Values
([(0,2),(2,1)],3)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => 2
([(2,3)],4)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 1
([(1,2),(1,3)],4)
 => [6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
 => ? = 1
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => 1
([(0,2),(0,3),(3,1)],4)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 2
([(1,2),(2,3)],4)
 => [4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => 2
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 2
([(1,3),(2,3)],4)
 => [6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
 => ? = 1
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => 2
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => 1
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 2
([(0,3),(1,2),(2,3)],4)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([],5)
 => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
([(3,4)],5)
 => [6,6,6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 2
([(2,3),(2,4)],5)
 => [6,6,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,2),(1,3),(1,4)],5)
 => [6,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
 => ? = 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [3,2,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => 2
([(2,4),(3,4)],5)
 => [6,6,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,4),(2,4),(3,4)],5)
 => [6,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
 => ? = 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [3,2,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 2
([(0,4),(1,4),(2,3)],5)
 => [6,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [8,3,2]
 => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => [6,5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => ? = 1
([(1,4),(2,3)],5)
 => [6,6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 1
([(1,4),(2,3),(2,4)],5)
 => [10,6]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [6,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
 => ? = 1
([(0,4),(1,2),(1,3)],5)
 => [6,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [6,5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => ? = 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => [8,3,2]
 => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
 => [1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [3,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => [10]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => 2
([],6)
 => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(4,5)],6)
 => [6,6,6,6,6,6,6,6]
 => ?
 => ?
 => ? = 1
([(3,4),(3,5)],6)
 => [6,6,6,6,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(2,3),(2,4),(2,5)],6)
 => [6,6,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [7,6,6,6]
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [7,6,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [7,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [14,6,6]
 => ?
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [7,6,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [14,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [4,4,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8,2,2]
 => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(2,3),(2,4),(4,5)],6)
 => [14,14]
 => ?
 => ?
 => ? = 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [14,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [7,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [4,4,4,4,2,2,2,2]
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [10,2,2]
 => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0]
 => ?
 => ? = 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [8,2]
 => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 2
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => 2
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => 2
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => [5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => [5,4,2]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => 2
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => 2
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 2
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => [5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => [5,4,2]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => 2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => 2
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
 => [5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
Description
The dominant dimension of the double dual of A/J when A is the corresponding Nakayama algebra with Jacobson radical J.
Matching statistic: St001217
Mapping
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
St001217: Dyck paths ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 67%
Values
([(0,2),(2,1)],3)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 1 = 2 - 1
([(2,3)],4)
 => [6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]
 => [1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]
 => ? = 1 - 1
([(1,2),(1,3)],4)
 => [6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => ? = 1 - 1
([(0,1),(0,2),(0,3)],4)
 => [3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => 0 = 1 - 1
([(0,2),(0,3),(3,1)],4)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(1,3),(2,3)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1 = 2 - 1
([(1,2),(2,3)],4)
 => [4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => 1 = 2 - 1
([(0,3),(3,1),(3,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1 = 2 - 1
([(1,3),(2,3)],4)
 => [6,2,2]
 => [1,1,1,1,0,0,1,1,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,0,0,1,0,0,0]
 => ? = 1 - 1
([(0,3),(1,3),(3,2)],4)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1 = 2 - 1
([(0,3),(1,3),(2,3)],4)
 => [3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => 0 = 1 - 1
([(0,3),(2,1),(3,2)],4)
 => [5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,1,0,0,0,0]
 => 1 = 2 - 1
([(0,3),(1,2),(2,3)],4)
 => [7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]
 => ? = 2 - 1
([],5)
 => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
 => ? = 1 - 1
([(3,4)],5)
 => [6,6,6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]
 => ? = 2 - 1
([(2,3),(2,4)],5)
 => [6,6,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [6,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [3,2,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [6,6,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]
 => ? = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [6,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
 => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0,0]
 => ? = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [3,2,2,2,2,2,2,2]
 => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]
 => [1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]
 => ? = 2 - 1
([(0,4),(1,4),(2,3)],5)
 => [6,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => ? = 1 - 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => [8,3,2]
 => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 0 = 1 - 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => [3,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => ? = 1 - 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,4),(2,3),(2,4)],5)
 => [6,5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
 => ? = 1 - 1
([(1,4),(2,3)],5)
 => [6,6,6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]
 => ? = 1 - 1
([(1,4),(2,3),(2,4)],5)
 => [10,6]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0]
 => ? = 1 - 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => [6,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,1,1,0,0,1,0,0,0]
 => ? = 1 - 1
([(0,4),(1,2),(1,3)],5)
 => [6,3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,1,1,0,0,1,0,0]
 => ? = 1 - 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => [6,5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,1,0,0]
 => ? = 1 - 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
 => ? = 2 - 1
([(0,3),(0,4),(1,2),(1,4)],5)
 => [8,3,2]
 => [1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]
 => ? = 1 - 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [5,3,2,2]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 0 = 1 - 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => [3,2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
 => ? = 1 - 1
([(1,4),(3,2),(4,3)],5)
 => [10]
 => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]
 => ? = 2 - 1
([(0,3),(3,4),(4,1),(4,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,2),(2,4),(4,3)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
 => ? = 2 - 1
([(0,4),(3,2),(4,1),(4,3)],5)
 => [8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]
 => ? = 2 - 1
([(0,4),(2,3),(3,1),(4,2)],5)
 => [6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 2 - 1
([(0,4),(1,2),(2,3),(3,4)],5)
 => [5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 1 = 2 - 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([],6)
 => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(4,5)],6)
 => [6,6,6,6,6,6,6,6]
 => ?
 => ?
 => ? = 1 - 1
([(3,4),(3,5)],6)
 => [6,6,6,6,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(2,3),(2,4),(2,5)],6)
 => [6,6,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [7,6,6,6]
 => ?
 => ?
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [7,6,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [7,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [4,2,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [14,6,6]
 => ?
 => ?
 => ? = 1 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [7,6,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [14,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [4,4,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => [8,2,2]
 => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]
 => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [14,14]
 => ?
 => ?
 => ? = 1 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [14,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [7,2,2,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [4,4,4,4,2,2,2,2]
 => ?
 => ?
 => ? = 1 - 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [10,2,2]
 => [1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0]
 => ?
 => ? = 2 - 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => [8,2]
 => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
 => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]
 => ? = 2 - 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)
 => [5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)
 => [5,2,2,2]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
 => [5,4,2]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => [5,4,2,2]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
 => [5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)
 => [5,4,2]
 => [1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
 => [5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)
 => [5,3,3]
 => [1,1,1,0,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => 1 = 2 - 1
Description
The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1.
Matching statistic: St000097
Mapping
Mp00195: Posets —order ideals⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St000097: Graphs ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 33%
Values
([(0,2),(2,1)],3)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
([(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
 => ([(0,2),(0,3),(0,4),(1,5),(1,6),(2,7),(2,9),(3,7),(3,8),(4,1),(4,8),(4,9),(5,11),(6,11),(7,10),(8,5),(8,10),(9,6),(9,10),(10,11)],12)
 => ([(0,4),(0,5),(0,9),(1,2),(1,3),(1,9),(2,6),(2,11),(3,6),(3,10),(4,7),(4,10),(5,7),(5,11),(6,8),(7,8),(8,10),(8,11),(9,10),(9,11)],12)
 => ? = 1
([(1,2),(1,3)],4)
 => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
 => ([(0,3),(0,4),(1,6),(1,8),(2,6),(2,7),(3,5),(4,1),(4,2),(4,5),(5,7),(5,8),(6,9),(7,9),(8,9)],10)
 => ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
 => ? = 1
([(0,1),(0,2),(0,3)],4)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,4),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,1),(4,2),(4,3),(5,8),(6,8),(7,8)],9)
 => ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
 => ? = 1
([(0,2),(0,3),(3,1)],4)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 2
([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(1,2),(2,3)],4)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
 => 2
([(0,3),(3,1),(3,2)],4)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 2
([(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
 => ([(0,2),(0,3),(0,4),(1,7),(2,6),(2,8),(3,5),(3,8),(4,5),(4,6),(5,9),(6,9),(8,1),(8,9),(9,7)],10)
 => ([(0,1),(0,9),(1,8),(2,3),(2,4),(2,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8),(6,9),(7,9),(8,9)],10)
 => ? = 1
([(0,3),(1,3),(3,2)],4)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
 => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => 2
([(0,3),(1,3),(2,3)],4)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
 => ([(0,8),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8)],9)
 => ? = 1
([(0,3),(2,1),(3,2)],4)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(1,3),(2,3),(2,4)],5)
 => 2
([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)
 => 2
([],5)
 => ?
 => ?
 => ?
 => ? = 1
([(3,4)],5)
 => ?
 => ?
 => ?
 => ? = 2
([(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
 => ([(0,1),(0,2),(0,3),(1,11),(1,13),(2,11),(2,12),(3,4),(3,5),(3,12),(3,13),(4,7),(4,9),(4,10),(5,6),(5,8),(5,10),(6,15),(6,17),(7,15),(7,18),(8,16),(8,17),(9,16),(9,18),(10,15),(10,16),(11,14),(12,6),(12,7),(12,14),(13,8),(13,9),(13,14),(14,17),(14,18),(15,19),(16,19),(17,19),(18,19)],20)
 => ([(0,2),(0,3),(0,19),(1,2),(1,3),(1,18),(2,17),(3,16),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,10),(5,11),(6,12),(6,13),(7,14),(7,15),(8,13),(8,15),(8,16),(9,12),(9,14),(9,16),(10,12),(10,14),(10,17),(11,13),(11,15),(11,17),(12,18),(13,18),(14,19),(15,19),(16,18),(16,19),(17,18),(17,19)],20)
 => ? = 2
([(1,2),(1,3),(1,4)],5)
 => ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
 => ([(0,1),(0,2),(1,12),(2,3),(2,4),(2,5),(2,12),(3,8),(3,10),(3,11),(4,7),(4,9),(4,11),(5,6),(5,9),(5,10),(6,13),(6,14),(7,13),(7,15),(8,14),(8,15),(9,13),(9,16),(10,14),(10,16),(11,15),(11,16),(12,6),(12,7),(12,8),(13,17),(14,17),(15,17),(16,17)],18)
 => ([(0,1),(0,17),(1,16),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,17)],18)
 => ? = 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ([(0,1),(1,2),(1,3),(1,4),(1,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ([(0,16),(1,5),(1,9),(1,10),(1,11),(2,5),(2,7),(2,8),(2,11),(3,5),(3,6),(3,8),(3,10),(4,5),(4,6),(4,7),(4,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 2
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 2
([(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(1,7),(2,11),(2,12),(2,13),(3,9),(3,10),(3,13),(4,8),(4,10),(4,12),(5,8),(5,9),(5,11),(6,16),(7,16),(8,1),(8,17),(8,18),(9,14),(9,17),(10,15),(10,17),(11,14),(11,18),(12,15),(12,18),(13,14),(13,15),(14,19),(15,19),(17,6),(17,19),(18,7),(18,19),(19,16)],20)
 => ([(0,2),(0,3),(0,19),(1,2),(1,3),(1,18),(2,17),(3,16),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,10),(5,11),(6,12),(6,13),(7,14),(7,15),(8,13),(8,15),(8,16),(9,12),(9,14),(9,16),(10,12),(10,14),(10,17),(11,13),(11,15),(11,17),(12,18),(13,18),(14,19),(15,19),(16,18),(16,19),(17,18),(17,19)],20)
 => ? = 2
([(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
 => ([(0,2),(0,3),(0,4),(0,5),(1,6),(2,7),(2,8),(2,9),(3,9),(3,11),(3,12),(4,8),(4,10),(4,12),(5,7),(5,10),(5,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,1),(16,17),(17,6)],18)
 => ([(0,1),(0,17),(1,16),(2,3),(2,4),(2,5),(2,6),(3,7),(3,8),(3,9),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,13),(7,14),(8,13),(8,15),(9,14),(9,15),(10,13),(10,16),(11,14),(11,16),(12,15),(12,16),(13,17),(14,17),(15,17),(16,17)],18)
 => ? = 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ([(0,2),(0,3),(0,4),(0,5),(2,9),(2,10),(2,11),(3,7),(3,8),(3,11),(4,6),(4,8),(4,10),(5,6),(5,7),(5,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16),(16,1)],17)
 => ([(0,16),(1,5),(1,9),(1,10),(1,11),(2,5),(2,7),(2,8),(2,11),(3,5),(3,6),(3,8),(3,10),(4,5),(4,6),(4,7),(4,9),(6,12),(6,15),(7,12),(7,13),(8,12),(8,14),(9,13),(9,15),(10,14),(10,15),(11,13),(11,14),(12,16),(13,16),(14,16),(15,16)],17)
 => ? = 2
([(0,4),(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
 => ([(0,3),(0,4),(0,5),(1,10),(2,7),(2,8),(3,9),(3,12),(4,9),(4,11),(5,2),(5,11),(5,12),(7,14),(8,14),(9,1),(9,13),(10,6),(11,7),(11,13),(12,8),(12,13),(13,10),(13,14),(14,6)],15)
 => ([(0,8),(0,13),(1,8),(1,12),(2,4),(2,5),(2,11),(3,6),(3,7),(3,11),(4,10),(4,12),(5,9),(5,12),(6,9),(6,13),(7,10),(7,13),(8,14),(9,11),(9,14),(10,11),(10,14),(12,14),(13,14)],15)
 => ? = 1
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
 => ([(0,3),(0,4),(0,5),(1,11),(2,10),(3,8),(3,9),(4,7),(4,8),(5,7),(5,9),(7,12),(8,2),(8,12),(9,1),(9,12),(10,6),(11,6),(12,10),(12,11)],13)
 => ([(0,8),(0,9),(1,9),(1,11),(2,8),(2,10),(3,5),(3,6),(3,7),(4,5),(4,6),(4,12),(5,10),(6,11),(7,10),(7,11),(8,12),(9,12),(10,12),(11,12)],13)
 => ? = 1
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
 => ([(0,3),(0,4),(0,5),(1,9),(2,8),(3,7),(3,10),(4,6),(4,10),(5,6),(5,7),(6,11),(7,11),(8,9),(10,2),(10,11),(11,1),(11,8)],12)
 => ([(0,9),(0,10),(1,2),(1,9),(2,11),(3,4),(3,5),(3,6),(4,7),(4,8),(5,8),(5,11),(6,7),(6,11),(7,10),(8,10),(9,11),(10,11)],12)
 => ? = 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
 => ([(0,3),(0,4),(0,5),(1,6),(2,6),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(7,10),(8,10),(9,10),(10,1),(10,2)],11)
 => ([(0,2),(0,10),(1,2),(1,10),(3,4),(3,5),(3,6),(4,8),(4,9),(5,7),(5,9),(6,7),(6,8),(7,10),(8,10),(9,10)],11)
 => ? = 1
([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 2
([(0,4),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)
 => ([(0,3),(0,4),(0,5),(1,8),(2,6),(2,7),(3,9),(3,11),(4,9),(4,10),(5,2),(5,10),(5,11),(6,13),(7,13),(9,12),(10,6),(10,12),(11,7),(11,12),(12,1),(12,13),(13,8)],14)
 => ([(0,1),(0,12),(1,13),(2,5),(2,6),(2,13),(3,5),(3,6),(3,11),(4,7),(4,8),(4,11),(5,10),(6,9),(7,9),(7,12),(8,10),(8,12),(9,11),(9,13),(10,11),(10,13),(12,13)],14)
 => ? = 1
([(1,4),(2,3)],5)
 => ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
 => ([(0,3),(0,4),(0,5),(1,8),(1,10),(2,7),(2,9),(3,11),(3,12),(4,2),(4,11),(4,13),(5,1),(5,12),(5,13),(6,17),(7,15),(8,16),(9,6),(9,15),(10,6),(10,16),(11,7),(11,14),(12,8),(12,14),(13,9),(13,10),(13,14),(14,15),(14,16),(15,17),(16,17)],18)
 => ([(0,7),(0,10),(0,11),(1,4),(1,8),(1,9),(2,6),(2,9),(2,11),(3,5),(3,8),(3,10),(4,12),(4,13),(5,12),(5,14),(6,13),(6,15),(7,14),(7,15),(8,12),(8,17),(9,13),(9,17),(10,14),(10,17),(11,15),(11,17),(12,16),(13,16),(14,16),(15,16),(16,17)],18)
 => ? = 1
([(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)
 => ([(0,3),(0,4),(0,5),(1,6),(1,7),(2,8),(2,10),(3,9),(3,11),(4,9),(4,12),(5,2),(5,11),(5,12),(6,14),(7,14),(8,13),(9,15),(10,6),(10,13),(11,8),(11,15),(12,1),(12,10),(12,15),(13,14),(15,7),(15,13)],16)
 => ([(0,3),(0,5),(0,14),(1,2),(1,4),(1,14),(2,6),(2,15),(3,7),(3,15),(4,6),(4,10),(5,7),(5,11),(6,12),(7,13),(8,9),(8,12),(8,13),(9,10),(9,11),(10,12),(10,14),(11,13),(11,14),(12,15),(13,15),(14,15)],16)
 => ? = 1
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
 => ([(0,3),(0,4),(0,5),(1,6),(1,8),(2,6),(2,7),(3,10),(3,11),(4,9),(4,11),(5,9),(5,10),(6,12),(7,12),(8,12),(9,13),(10,13),(11,1),(11,2),(11,13),(13,7),(13,8)],14)
 => ([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,8),(2,9),(3,10),(3,11),(4,9),(4,13),(5,8),(5,13),(6,11),(6,13),(7,10),(7,13),(8,12),(9,12),(10,12),(11,12),(12,13)],14)
 => ? = 1
([(0,4),(1,2),(1,3)],5)
 => ([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15)
 => ([(0,2),(0,3),(1,11),(2,1),(2,12),(3,4),(3,5),(3,12),(4,8),(4,10),(5,8),(5,9),(6,14),(7,14),(8,13),(9,6),(9,13),(10,7),(10,13),(11,6),(11,7),(12,9),(12,10),(12,11),(13,14)],15)
 => ([(0,8),(0,13),(1,8),(1,12),(2,4),(2,5),(2,11),(3,6),(3,7),(3,11),(4,10),(4,12),(5,9),(5,12),(6,9),(6,13),(7,10),(7,13),(8,14),(9,11),(9,14),(10,11),(10,14),(12,14),(13,14)],15)
 => ? = 1
([(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)
 => ([(0,1),(0,2),(1,11),(2,4),(2,5),(2,11),(3,6),(3,7),(4,8),(4,10),(5,8),(5,9),(6,13),(7,13),(8,12),(9,6),(9,12),(10,7),(10,12),(11,3),(11,9),(11,10),(12,13)],14)
 => ([(0,1),(0,12),(1,13),(2,5),(2,6),(2,13),(3,5),(3,6),(3,11),(4,7),(4,8),(4,11),(5,10),(6,9),(7,9),(7,12),(8,10),(8,12),(9,11),(9,13),(10,11),(10,13),(12,13)],14)
 => ? = 1
([(0,2),(0,4),(3,1),(4,3)],5)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,5),(1,6),(2,7),(3,4),(3,6),(4,2),(4,8),(5,1),(5,3),(6,8),(8,7)],9)
 => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
 => 2
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8)
 => ([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)
 => 2
([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13)
 => ([(0,3),(0,4),(1,11),(2,10),(3,2),(3,9),(4,1),(4,9),(5,7),(5,8),(6,12),(7,12),(8,12),(9,5),(9,10),(9,11),(10,6),(10,7),(11,6),(11,8)],13)
 => ([(0,8),(0,9),(1,9),(1,11),(2,8),(2,10),(3,5),(3,6),(3,7),(4,5),(4,6),(4,12),(5,10),(6,11),(7,10),(7,11),(8,12),(9,12),(10,12),(11,12)],13)
 => ? = 1
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(1,9),(2,7),(2,8),(3,6),(4,10),(5,3),(5,10),(6,8),(6,9),(7,11),(8,11),(9,11),(10,1),(10,2),(10,6)],12)
 => ([(0,4),(0,5),(1,7),(1,9),(2,7),(2,8),(3,6),(4,10),(5,3),(5,10),(6,8),(6,9),(7,11),(8,11),(9,11),(10,1),(10,2),(10,6)],12)
 => ([(0,9),(0,10),(1,2),(1,9),(2,11),(3,4),(3,5),(3,6),(4,7),(4,8),(5,8),(5,11),(6,7),(6,11),(7,10),(8,10),(9,11),(10,11)],12)
 => ? = 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => ([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)
 => ([(0,4),(0,5),(1,7),(1,8),(2,6),(2,8),(3,6),(3,7),(4,9),(5,9),(6,10),(7,10),(8,10),(9,1),(9,2),(9,3)],11)
 => ([(0,2),(0,10),(1,2),(1,10),(3,4),(3,5),(3,6),(4,8),(4,9),(5,7),(5,9),(6,7),(6,8),(7,10),(8,10),(9,10)],11)
 => ? = 1
([(1,4),(3,2),(4,3)],5)
 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
 => ([(0,3),(0,7),(1,2),(1,6),(2,8),(3,9),(4,5),(4,8),(4,9),(5,6),(5,7),(6,8),(7,9)],10)
 => 2
([(0,3),(3,4),(4,1),(4,2)],5)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
 => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 2
([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => 2
([(0,4),(3,2),(4,1),(4,3)],5)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)
 => ([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)
 => 2
([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
 => 2
([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
 => ([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)
 => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
 => ([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)
 => 2
([],6)
 => ?
 => ?
 => ?
 => ? = 1
([(4,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(3,4),(3,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(2,3),(2,4),(2,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(1,3),(1,4),(1,5),(1,6),(2,7),(3,8),(3,9),(3,10),(4,10),(4,12),(4,13),(5,9),(5,11),(5,13),(6,8),(6,11),(6,12),(8,14),(8,15),(9,14),(9,16),(10,15),(10,16),(11,14),(11,17),(12,15),(12,17),(13,16),(13,17),(14,18),(15,18),(16,18),(17,2),(17,18),(18,7)],19)
 => ?
 => ?
 => ? = 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
 => ([(0,6),(2,10),(2,11),(2,12),(3,8),(3,9),(3,12),(4,7),(4,9),(4,11),(5,7),(5,8),(5,10),(6,2),(6,3),(6,4),(6,5),(7,13),(7,16),(8,13),(8,14),(9,13),(9,15),(10,14),(10,16),(11,15),(11,16),(12,14),(12,15),(13,17),(14,17),(15,17),(16,17),(17,1)],18)
 => ?
 => ? = 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(1,7),(2,14),(3,4),(3,5),(3,6),(3,14),(4,10),(4,12),(4,13),(5,9),(5,11),(5,13),(6,8),(6,11),(6,12),(8,15),(8,16),(9,15),(9,17),(10,16),(10,17),(11,15),(11,18),(12,16),(12,18),(13,17),(13,18),(14,8),(14,9),(14,10),(15,19),(16,19),(17,19),(18,1),(18,19),(19,7)],20)
 => ?
 => ?
 => ? = 1
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)
 => ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
 => ([(0,6),(2,8),(2,9),(3,7),(3,9),(4,7),(4,8),(5,1),(6,2),(6,3),(6,4),(7,10),(8,10),(9,10),(10,5)],11)
 => ?
 => ? = 2
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
 => ([(0,6),(2,10),(3,8),(3,9),(4,7),(4,9),(5,7),(5,8),(6,3),(6,4),(6,5),(7,11),(8,11),(9,2),(9,11),(10,1),(11,10)],12)
 => ?
 => ? = 2
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)
 => ([(0,6),(1,11),(2,7),(2,8),(3,8),(3,9),(4,7),(4,9),(5,1),(5,10),(6,2),(6,3),(6,4),(7,12),(8,12),(9,5),(9,12),(10,11),(12,10)],13)
 => ?
 => ?
 => ? = 2
([(2,3),(2,4),(4,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => ([(0,1),(1,2),(1,3),(2,13),(3,4),(3,5),(3,6),(3,13),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,14),(7,15),(8,14),(8,16),(9,15),(9,16),(10,14),(10,17),(11,15),(11,17),(12,16),(12,17),(13,7),(13,8),(13,9),(14,18),(15,18),(16,18),(17,18)],19)
 => ([(0,1),(1,2),(1,3),(2,13),(3,4),(3,5),(3,6),(3,13),(4,9),(4,11),(4,12),(5,8),(5,10),(5,12),(6,7),(6,10),(6,11),(7,14),(7,15),(8,14),(8,16),(9,15),(9,16),(10,14),(10,17),(11,15),(11,17),(12,16),(12,17),(13,7),(13,8),(13,9),(14,18),(15,18),(16,18),(17,18)],19)
 => ?
 => ? = 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => ?
 => ?
 => ?
 => ? = 1
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)
 => ([(0,4),(0,6),(1,10),(2,8),(2,12),(3,8),(3,11),(4,7),(5,1),(5,9),(6,2),(6,3),(6,7),(7,11),(7,12),(8,5),(8,13),(9,10),(11,13),(12,13),(13,9)],14)
 => ?
 => ?
 => ? = 2
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9)
 => ([(0,6),(1,8),(2,8),(3,7),(4,7),(5,3),(5,4),(6,1),(6,2),(8,5)],9)
 => ?
 => ? = 2
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
 => ([(0,6),(1,9),(2,9),(3,8),(4,7),(5,3),(5,7),(6,1),(6,2),(7,8),(9,4),(9,5)],10)
 => ?
 => ?
 => ? = 2
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
 => ([(0,6),(1,9),(2,8),(3,5),(3,7),(4,1),(4,7),(5,2),(5,10),(6,3),(6,4),(7,9),(7,10),(8,12),(9,11),(10,8),(10,11),(11,12)],13)
 => ([(0,10),(1,6),(1,8),(2,5),(2,9),(3,7),(3,9),(4,7),(4,10),(4,12),(5,6),(5,11),(6,12),(7,11),(8,10),(8,12),(9,11),(11,12)],13)
 => 2
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(0,6),(1,7),(2,9),(4,8),(5,1),(5,9),(6,2),(6,5),(7,8),(8,3),(9,4),(9,7)],10)
 => ([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10)
 => 2
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11)
 => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,5),(4,10),(5,2),(5,9),(6,1),(6,3),(7,10),(9,8),(10,9)],11)
 => ([(0,10),(1,6),(1,10),(2,3),(2,8),(3,9),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(7,10),(8,9)],11)
 => 2
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
 => 2
([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
 => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
 => ([(0,7),(2,9),(3,10),(4,8),(5,4),(5,10),(6,1),(7,3),(7,5),(8,9),(9,6),(10,2),(10,8)],11)
 => ([(0,9),(1,5),(2,9),(2,10),(3,7),(3,10),(4,6),(4,8),(5,7),(6,9),(6,10),(7,8),(8,10)],11)
 => 2
([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
 => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11)
 => ([(0,6),(1,8),(2,10),(4,9),(5,1),(5,10),(6,7),(7,2),(7,5),(8,9),(9,3),(10,4),(10,8)],11)
 => ([(0,9),(1,5),(2,9),(2,10),(3,7),(3,10),(4,6),(4,8),(5,7),(6,9),(6,10),(7,8),(8,10)],11)
 => 2
([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
 => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
 => 2
Description
The order of the largest clique of the graph. A clique in a graph $G$ is a subset $U \subseteq V(G)$ such that any pair of vertices in $U$ are adjacent. I.e. the subgraph induced by $U$ is a complete graph.
The following 21 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St001712The number of natural descents of a standard Young tableau. St000098The chromatic number of a graph. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St001462The number of factors of a standard tableaux under concatenation. St001060The distinguishing index of a graph. St001570The minimal number of edges to add to make a graph Hamiltonian. St000264The girth of a graph, which is not a tree. St000699The toughness times the least common multiple of 1,. St000456The monochromatic index of a connected graph. St001118The acyclic chromatic index of a graph. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St001629The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles. St001545The second Elser number of a connected graph. St000464The Schultz index of a connected graph.