Processing math: 100%

Your data matches 220 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000993
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000993: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],4)
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 4
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 3
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 2
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 2
Description
The multiplicity of the largest part of an integer partition.
Matching statistic: St001506
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001506: Dyck paths ⟶ ℤResult quality: 88% ●values known / values provided: 88%●distinct values known / distinct values provided: 100%
Values
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([],6)
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 5 = 4 + 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => 4 = 3 + 1
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => 3 = 2 + 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => 3 = 2 + 1
([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9)
 => [5,1,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9)
 => [4,2,1,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9)
 => [4,2,1,1,1]
 => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [7,5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
 => ? = 1 + 1
([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => [5,3,3,1]
 => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]
 => ? = 1 + 1
([(0,18),(1,19),(2,18),(2,22),(3,19),(3,22),(4,6),(6,5),(7,11),(8,16),(9,17),(10,13),(10,14),(11,4),(12,23),(13,8),(13,23),(14,9),(14,23),(15,11),(16,15),(17,7),(17,15),(18,20),(19,21),(20,12),(20,13),(21,12),(21,14),(22,10),(22,20),(22,21),(23,16),(23,17)],24)
 => [11,7,5,1]
 => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0]
 => ? = 1 + 1
([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => [5,4,3,2,1]
 => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
([(0,18),(1,17),(2,18),(2,24),(3,23),(3,24),(4,17),(4,23),(6,15),(7,16),(8,9),(9,5),(10,12),(11,13),(12,11),(13,14),(14,9),(15,7),(15,21),(16,8),(16,14),(17,10),(18,6),(18,19),(19,15),(19,22),(20,12),(20,22),(21,13),(21,16),(22,11),(22,21),(23,10),(23,20),(24,19),(24,20)],25)
 => [9,7,5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
 => ? = 1 + 1
([(0,13),(1,16),(2,15),(3,13),(3,17),(4,15),(4,16),(4,17),(6,10),(7,19),(8,19),(9,18),(10,5),(11,7),(11,18),(12,8),(12,18),(13,14),(14,7),(14,8),(15,9),(15,11),(16,9),(16,12),(17,11),(17,12),(17,14),(18,6),(18,19),(19,10)],20)
 => [7,5,4,3,1]
 => [1,0,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0]
 => ? = 1 + 1
([(0,14),(1,13),(2,18),(2,20),(3,19),(3,20),(4,13),(4,18),(5,14),(5,19),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,17),(16,10),(16,17),(17,11),(17,12),(18,7),(18,15),(19,8),(19,16),(20,15),(20,16)],21)
 => [6,5,4,3,2,1]
 => [1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]
 => [1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => [4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,7),(2,7),(3,7),(4,7),(5,6),(7,6)],8)
 => [4,1,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]
 => ? = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,6),(4,7),(5,7),(7,6)],8)
 => [5,1,1,1]
 => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => [5,2,1,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => [5,2,1,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => [5,2,1,1]
 => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
 => [5,3,2,2]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => [5,3,2,2,2]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => ?
 => ? = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => [5,3,2,2]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => [5,3,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => [5,3,2,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => [5,3,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => [5,3,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
 => [5,3,2,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
 => [5,3,2,2,2]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
 => ?
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
 => [5,3,2,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
 => [5,3,2,2,2,1]
 => [1,0,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]
 => [1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0,1,0]
 => ? = 3 + 1
([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => [6,4,2]
 => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]
 => ? = 1 + 1
([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
 => [7,5,3]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
 => [7,5,3,1]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]
 => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0,0,1,0]
 => ? = 1 + 1
([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14)
 => [7,4,3]
 => [1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,0]
 => ? = 1 + 1
([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16)
 => [8,5,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19)
 => [9,6,4]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
 => [10,6,4]
 => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
 => [8,6,4,2]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15)
 => [7,5,3]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15)
 => [8,5,2]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0,0]
 => ? = 1 + 1
([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18)
 => [9,6,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20)
 => [10,7,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21)
 => [11,7,3]
 => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(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)
 => [7,4,2]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]
 => ? = 1 + 1
([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19)
 => [8,5,4,2]
 => [1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => [9,6,5,3]
 => [1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => [10,7,5,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22)
 => [9,6,4,3]
 => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
 => [7,5,2]
 => [1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
 => ? = 1 + 1
([(0,7),(0,8),(1,10),(1,16),(2,11),(3,10),(4,12),(4,13),(5,3),(6,2),(6,16),(7,9),(8,5),(9,1),(9,6),(10,14),(11,12),(11,15),(12,17),(13,17),(14,13),(14,15),(15,17),(16,4),(16,11),(16,14)],18)
 => [8,6,4]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,8),(0,9),(1,15),(1,18),(2,13),(3,11),(3,17),(4,11),(5,12),(6,4),(7,5),(7,17),(8,10),(9,6),(10,3),(10,7),(11,14),(12,16),(12,18),(14,15),(14,16),(15,19),(16,19),(17,1),(17,12),(17,14),(18,2),(18,19),(19,13)],20)
 => [9,7,4]
 => [1,0,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0]
 => ?
 => ? = 1 + 1
([(0,10),(0,12),(1,23),(2,22),(3,14),(3,24),(4,15),(5,13),(5,14),(6,18),(7,16),(7,20),(8,5),(8,23),(9,4),(9,24),(10,11),(11,3),(11,9),(12,1),(12,8),(13,22),(14,19),(15,16),(15,21),(16,25),(18,17),(19,20),(19,21),(20,18),(20,25),(21,25),(22,6),(23,2),(23,13),(24,7),(24,15),(24,19),(25,17)],26)
 => [9,7,5,4,1]
 => [1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]
 => ?
 => ? = 1 + 1
([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,5),(5,1),(5,10),(6,4),(7,8),(8,2),(8,3),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
 => [7,5,2]
 => [1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]
 => ? = 1 + 1
Description
Half the projective dimension of the unique simple module with even projective dimension in a magnitude 1 Nakayama algebra.
Matching statistic: St000733
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00155: Standard tableaux —promotion⟶ Standard tableaux
St000733: Standard tableaux ⟶ ℤResult quality: 86% ●values known / values provided: 86%●distinct values known / distinct values provided: 100%
Values
([],4)
 => [1,1,1,1]
 => [[1],[2],[3],[4]]
 => [[1],[2],[3],[4]]
 => 4 = 2 + 2
([],5)
 => [1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [[1],[2],[3],[4],[5]]
 => 5 = 3 + 2
([(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3],[2],[4],[5]]
 => 4 = 2 + 2
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3],[2],[4],[5]]
 => 4 = 2 + 2
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3],[2],[4],[5]]
 => 4 = 2 + 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3],[2],[4],[5]]
 => 4 = 2 + 2
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3],[2],[4],[5]]
 => 4 = 2 + 2
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3],[2],[4],[5]]
 => 4 = 2 + 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [[1,3],[2],[4],[5]]
 => 4 = 2 + 2
([],6)
 => [1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => [[1],[2],[3],[4],[5],[6]]
 => 6 = 4 + 2
([(4,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [[1,3],[2],[4],[5],[6]]
 => 5 = 3 + 2
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [[1,3,4],[2],[5],[6]]
 => 4 = 2 + 2
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [[1,3],[2,5],[4],[6]]
 => 4 = 2 + 2
([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9)
 => [5,1,1,1,1]
 => [[1,2,3,4,5],[6],[7],[8],[9]]
 => [[1,3,4,5,6],[2],[7],[8],[9]]
 => ? = 3 + 2
([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9)
 => [4,2,1,1,1]
 => [[1,2,3,4],[5,6],[7],[8],[9]]
 => [[1,3,4,5],[2,7],[6],[8],[9]]
 => ? = 3 + 2
([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9)
 => [4,2,1,1,1]
 => [[1,2,3,4],[5,6],[7],[8],[9]]
 => [[1,3,4,5],[2,7],[6],[8],[9]]
 => ? = 3 + 2
([(0,8),(1,7),(2,7),(2,9),(3,8),(3,9),(5,4),(6,4),(7,5),(8,6),(9,5),(9,6)],10)
 => [4,3,2,1]
 => [[1,2,3,4],[5,6,7],[8,9],[10]]
 => [[1,3,4,5],[2,7,8],[6,10],[9]]
 => ? = 1 + 2
([(0,13),(1,12),(2,13),(2,15),(3,12),(3,15),(5,11),(6,7),(7,4),(8,9),(9,10),(10,7),(11,6),(11,10),(12,8),(13,5),(13,14),(14,9),(14,11),(15,8),(15,14)],16)
 => [7,5,3,1]
 => [[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15],[16]]
 => ?
 => ? = 1 + 2
([(0,10),(1,9),(2,8),(3,8),(3,9),(3,10),(5,11),(6,11),(7,11),(8,5),(8,6),(9,5),(9,7),(10,6),(10,7),(11,4)],12)
 => [5,3,3,1]
 => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]]
 => [[1,3,4,5,6],[2,8,9],[7,11,12],[10]]
 => ? = 1 + 2
([(0,18),(1,19),(2,18),(2,22),(3,19),(3,22),(4,6),(6,5),(7,11),(8,16),(9,17),(10,13),(10,14),(11,4),(12,23),(13,8),(13,23),(14,9),(14,23),(15,11),(16,15),(17,7),(17,15),(18,20),(19,21),(20,12),(20,13),(21,12),(21,14),(22,10),(22,20),(22,21),(23,16),(23,17)],24)
 => [11,7,5,1]
 => [[1,2,3,4,5,6,7,8,9,10,11],[12,13,14,15,16,17,18],[19,20,21,22,23],[24]]
 => ?
 => ? = 1 + 2
([(0,11),(1,10),(2,10),(2,13),(3,11),(3,14),(4,13),(4,14),(6,8),(7,9),(8,5),(9,5),(10,6),(11,7),(12,8),(12,9),(13,6),(13,12),(14,7),(14,12)],15)
 => [5,4,3,2,1]
 => [[1,2,3,4,5],[6,7,8,9],[10,11,12],[13,14],[15]]
 => [[1,3,4,5,6],[2,8,9,10],[7,12,13],[11,15],[14]]
 => ? = 1 + 2
([(0,18),(1,17),(2,18),(2,24),(3,23),(3,24),(4,17),(4,23),(6,15),(7,16),(8,9),(9,5),(10,12),(11,13),(12,11),(13,14),(14,9),(15,7),(15,21),(16,8),(16,14),(17,10),(18,6),(18,19),(19,15),(19,22),(20,12),(20,22),(21,13),(21,16),(22,11),(22,21),(23,10),(23,20),(24,19),(24,20)],25)
 => [9,7,5,3,1]
 => [[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15,16],[17,18,19,20,21],[22,23,24],[25]]
 => ?
 => ? = 1 + 2
([(0,13),(1,16),(2,15),(3,13),(3,17),(4,15),(4,16),(4,17),(6,10),(7,19),(8,19),(9,18),(10,5),(11,7),(11,18),(12,8),(12,18),(13,14),(14,7),(14,8),(15,9),(15,11),(16,9),(16,12),(17,11),(17,12),(17,14),(18,6),(18,19),(19,10)],20)
 => [7,5,4,3,1]
 => [[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15,16],[17,18,19],[20]]
 => ?
 => ? = 1 + 2
([(0,14),(1,13),(2,18),(2,20),(3,19),(3,20),(4,13),(4,18),(5,14),(5,19),(7,9),(8,10),(9,11),(10,12),(11,6),(12,6),(13,7),(14,8),(15,9),(15,17),(16,10),(16,17),(17,11),(17,12),(18,7),(18,15),(19,8),(19,16),(20,15),(20,16)],21)
 => [6,5,4,3,2,1]
 => [[1,2,3,4,5,6],[7,8,9,10,11],[12,13,14,15],[16,17,18],[19,20],[21]]
 => ?
 => ? = 1 + 2
([(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)
 => [5,2,2]
 => [[1,2,3,4,5],[6,7],[8,9]]
 => [[1,3,4,5,6],[2,8],[7,9]]
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,7),(2,6),(3,5),(4,5),(4,6),(5,8),(6,8),(8,7)],9)
 => [5,2,1,1]
 => [[1,2,3,4,5],[6,7],[8],[9]]
 => [[1,3,4,5,6],[2,8],[7],[9]]
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,7),(4,6),(5,6),(5,7),(6,8),(7,8)],9)
 => [5,2,1,1]
 => [[1,2,3,4,5],[6,7],[8],[9]]
 => [[1,3,4,5,6],[2,8],[7],[9]]
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(4,7),(5,8),(6,7),(7,8)],9)
 => [5,2,1,1]
 => [[1,2,3,4,5],[6,7],[8],[9]]
 => [[1,3,4,5,6],[2,8],[7],[9]]
 => ? = 2 + 2
([(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)
 => [5,2,2]
 => [[1,2,3,4,5],[6,7],[8,9]]
 => [[1,3,4,5,6],[2,8],[7,9]]
 => ? = 1 + 2
([(0,2),(0,3),(0,4),(1,7),(1,9),(2,8),(3,5),(3,8),(4,1),(4,5),(4,8),(5,7),(5,9),(7,6),(8,9),(9,6)],10)
 => [5,3,2]
 => [[1,2,3,4,5],[6,7,8],[9,10]]
 => [[1,3,4,5,6],[2,8,9],[7,10]]
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(3,8),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => [5,3,2]
 => [[1,2,3,4,5],[6,7,8],[9,10]]
 => [[1,3,4,5,6],[2,8,9],[7,10]]
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,10),(2,6),(2,7),(2,10),(3,5),(3,7),(3,10),(4,5),(4,6),(4,10),(5,9),(5,11),(6,9),(6,11),(7,9),(7,11),(9,8),(10,11),(11,8)],12)
 => [5,3,2,2]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10,12]]
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,12),(2,8),(2,10),(2,12),(3,7),(3,10),(3,12),(4,6),(4,10),(4,12),(5,6),(5,7),(5,8),(5,12),(6,11),(6,13),(7,11),(7,13),(8,11),(8,13),(10,13),(11,9),(12,11),(12,13),(13,9)],14)
 => [5,3,2,2,2]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13,14]]
 => ?
 => ? = 3 + 2
([(0,1),(0,2),(0,3),(0,4),(1,6),(1,11),(2,5),(2,11),(3,5),(3,7),(3,11),(4,6),(4,7),(4,11),(5,9),(6,10),(7,9),(7,10),(9,8),(10,8),(11,9),(11,10)],12)
 => [5,3,2,2]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10,12]]
 => ? = 2 + 2
([(0,2),(0,3),(0,4),(1,9),(2,5),(2,7),(3,5),(3,6),(4,1),(4,6),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => [5,3,2,1]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10]]
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,10),(2,8),(2,9),(2,10),(3,7),(3,9),(3,10),(4,5),(4,7),(4,8),(5,11),(7,11),(7,12),(8,11),(8,12),(9,12),(10,11),(10,12),(11,6),(12,6)],13)
 => [5,3,2,2,1]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10,13],[12]]
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,6),(2,7),(2,8),(3,5),(3,7),(3,8),(5,9),(5,10),(6,9),(6,10),(7,10),(8,9),(8,10),(9,4),(10,4)],11)
 => [5,3,2,1]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10]]
 => ? = 1 + 2
([(0,1),(0,2),(0,3),(1,7),(1,8),(2,5),(2,8),(3,5),(3,7),(5,9),(6,4),(7,6),(7,9),(8,6),(8,9),(9,4)],10)
 => [5,3,2]
 => [[1,2,3,4,5],[6,7,8],[9,10]]
 => [[1,3,4,5,6],[2,8,9],[7,10]]
 => ? = 1 + 2
([(0,2),(0,3),(0,4),(1,9),(1,10),(2,6),(2,7),(3,5),(3,6),(4,1),(4,5),(4,7),(5,10),(6,9),(6,10),(7,9),(7,10),(9,8),(10,8)],11)
 => [5,3,2,1]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10]]
 => ? = 1 + 2
([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,9),(2,10),(3,6),(3,9),(4,7),(4,9),(4,10),(5,1),(5,6),(5,7),(5,10),(6,11),(6,12),(7,11),(7,12),(9,12),(10,11),(10,12),(11,8),(12,8)],13)
 => [5,3,2,2,1]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10,13],[12]]
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,10),(1,11),(2,6),(2,9),(2,11),(3,6),(3,9),(3,10),(4,7),(4,9),(4,10),(4,11),(5,7),(5,9),(5,10),(5,11),(6,13),(7,12),(7,13),(9,12),(9,13),(10,12),(10,13),(11,12),(11,13),(12,8),(13,8)],14)
 => [5,3,2,2,2]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13,14]]
 => ?
 => ? = 3 + 2
([(0,2),(0,3),(0,4),(0,5),(1,11),(1,12),(2,7),(2,10),(3,6),(3,10),(4,6),(4,8),(4,10),(5,1),(5,7),(5,8),(5,10),(6,12),(7,11),(7,12),(8,11),(8,12),(10,11),(10,12),(11,9),(12,9)],13)
 => [5,3,2,2,1]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13]]
 => [[1,3,4,5,6],[2,8,9],[7,11],[10,13],[12]]
 => ? = 2 + 2
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,9),(1,10),(1,11),(1,12),(2,7),(2,11),(2,12),(3,7),(3,9),(3,10),(4,6),(4,10),(4,12),(5,6),(5,9),(5,11),(6,14),(7,13),(9,13),(9,14),(10,13),(10,14),(11,13),(11,14),(12,13),(12,14),(13,8),(14,8)],15)
 => [5,3,2,2,2,1]
 => [[1,2,3,4,5],[6,7,8],[9,10],[11,12],[13,14],[15]]
 => ?
 => ? = 3 + 2
([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
 => [6,4,2]
 => [[1,2,3,4,5,6],[7,8,9,10],[11,12]]
 => [[1,3,4,5,6,7],[2,9,10,11],[8,12]]
 => ? = 1 + 2
([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
 => [7,5,3]
 => [[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15]]
 => ?
 => ? = 1 + 2
([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
 => [7,5,3,1]
 => [[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15],[16]]
 => ?
 => ? = 1 + 2
([(0,6),(1,9),(1,10),(2,8),(3,7),(4,3),(4,12),(5,2),(5,12),(6,4),(6,5),(7,9),(7,11),(8,10),(8,11),(9,13),(10,13),(11,13),(12,1),(12,7),(12,8)],14)
 => [7,4,3]
 => [[1,2,3,4,5,6,7],[8,9,10,11],[12,13,14]]
 => ?
 => ? = 1 + 2
([(0,7),(1,11),(1,14),(2,10),(3,8),(4,9),(5,3),(5,13),(6,4),(6,13),(7,5),(7,6),(8,12),(8,14),(9,11),(9,12),(11,15),(12,15),(13,1),(13,8),(13,9),(14,2),(14,15),(15,10)],16)
 => [8,5,3]
 => [[1,2,3,4,5,6,7,8],[9,10,11,12,13],[14,15,16]]
 => ?
 => ? = 1 + 2
([(0,1),(1,4),(1,5),(2,14),(3,13),(4,6),(4,17),(5,7),(5,17),(6,15),(7,16),(8,11),(8,12),(10,18),(11,3),(11,18),(12,2),(12,18),(13,9),(14,9),(15,10),(15,11),(16,10),(16,12),(17,8),(17,15),(17,16),(18,13),(18,14)],19)
 => [9,6,4]
 => [[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15],[16,17,18,19]]
 => ?
 => ? = 1 + 2
([(0,9),(2,16),(2,17),(3,13),(4,12),(5,10),(6,11),(7,5),(7,15),(8,6),(8,15),(9,7),(9,8),(10,14),(10,16),(11,14),(11,17),(12,18),(13,18),(14,19),(15,2),(15,10),(15,11),(16,4),(16,19),(17,3),(17,19),(18,1),(19,12),(19,13)],20)
 => [10,6,4]
 => [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16],[17,18,19,20]]
 => ?
 => ? = 1 + 2
([(0,9),(0,11),(1,18),(2,17),(3,19),(4,13),(4,19),(5,12),(5,13),(6,16),(7,14),(8,5),(8,18),(9,10),(10,3),(10,4),(11,1),(11,8),(12,17),(13,15),(15,16),(16,14),(17,7),(18,2),(18,12),(19,6),(19,15)],20)
 => [8,6,4,2]
 => [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14],[15,16,17,18],[19,20]]
 => ?
 => ? = 1 + 2
([(0,9),(0,10),(1,11),(2,14),(3,12),(4,13),(5,4),(5,11),(6,5),(7,3),(8,1),(8,14),(9,6),(10,2),(10,8),(11,13),(13,12),(14,7)],15)
 => [7,5,3]
 => [[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14,15]]
 => ?
 => ? = 1 + 2
([(0,7),(1,14),(2,9),(3,10),(4,5),(4,14),(5,6),(5,8),(6,2),(6,11),(7,1),(7,4),(8,10),(8,11),(9,13),(10,12),(11,9),(11,12),(12,13),(14,3),(14,8)],15)
 => [8,5,2]
 => [[1,2,3,4,5,6,7,8],[9,10,11,12,13],[14,15]]
 => ?
 => ? = 1 + 2
([(0,1),(1,4),(1,5),(2,13),(3,12),(4,14),(5,7),(5,14),(6,10),(7,8),(7,15),(8,6),(8,17),(10,11),(11,9),(12,9),(13,3),(13,16),(14,2),(14,15),(15,13),(15,17),(16,11),(16,12),(17,10),(17,16)],18)
 => [9,6,3]
 => [[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15],[16,17,18]]
 => ?
 => ? = 1 + 2
([(0,1),(1,5),(1,6),(2,15),(3,14),(4,10),(5,16),(6,8),(6,16),(7,12),(8,9),(8,17),(9,7),(9,19),(11,13),(12,11),(13,10),(14,4),(14,13),(15,3),(15,18),(16,2),(16,17),(17,15),(17,19),(18,11),(18,14),(19,12),(19,18)],20)
 => [10,7,3]
 => [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17],[18,19,20]]
 => ?
 => ? = 1 + 2
([(0,10),(1,20),(2,19),(4,18),(5,17),(6,13),(7,8),(7,17),(8,9),(8,11),(9,6),(9,15),(10,5),(10,7),(11,15),(11,18),(12,16),(12,20),(13,16),(14,19),(15,12),(15,13),(16,14),(17,4),(17,11),(18,1),(18,12),(19,3),(20,2),(20,14)],21)
 => [11,7,3]
 => [[1,2,3,4,5,6,7,8,9,10,11],[12,13,14,15,16,17,18],[19,20,21]]
 => ?
 => ? = 1 + 2
([(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)
 => [7,4,2]
 => [[1,2,3,4,5,6,7],[8,9,10,11],[12,13]]
 => ?
 => ? = 1 + 2
([(0,1),(1,2),(1,3),(2,4),(2,13),(3,6),(3,13),(4,15),(5,14),(6,5),(6,16),(7,10),(7,12),(8,18),(9,18),(10,17),(11,9),(11,17),(12,8),(12,17),(13,7),(13,15),(13,16),(14,8),(14,9),(15,10),(15,11),(16,11),(16,12),(16,14),(17,18)],19)
 => [8,5,4,2]
 => [[1,2,3,4,5,6,7,8],[9,10,11,12,13],[14,15,16,17],[18,19]]
 => ?
 => ? = 1 + 2
([(0,1),(1,2),(1,3),(2,4),(2,16),(3,6),(3,16),(4,18),(5,17),(6,5),(6,19),(7,9),(7,11),(8,10),(8,14),(9,21),(10,22),(11,21),(12,20),(13,12),(13,22),(14,7),(14,15),(14,22),(15,9),(15,20),(16,8),(16,18),(16,19),(17,12),(17,15),(18,10),(18,13),(19,13),(19,14),(19,17),(20,21),(22,11),(22,20)],23)
 => [9,6,5,3]
 => [[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15],[16,17,18,19,20],[21,22,23]]
 => ?
 => ? = 1 + 2
([(0,1),(1,3),(1,4),(2,14),(3,6),(3,20),(4,5),(4,20),(5,19),(6,7),(6,21),(7,18),(8,12),(8,13),(9,11),(9,17),(10,22),(11,24),(12,23),(13,2),(13,23),(15,13),(15,22),(16,10),(16,24),(17,8),(17,15),(17,24),(18,10),(18,15),(19,11),(19,16),(20,9),(20,19),(20,21),(21,16),(21,17),(21,18),(22,23),(23,14),(24,12),(24,22)],25)
 => [10,7,5,3]
 => [[1,2,3,4,5,6,7,8,9,10],[11,12,13,14,15,16,17],[18,19,20,21,22],[23,24,25]]
 => ?
 => ? = 1 + 2
([(0,1),(1,3),(1,4),(2,15),(3,6),(3,18),(4,5),(4,18),(5,17),(6,7),(6,19),(7,16),(8,12),(8,14),(10,21),(11,21),(12,2),(12,20),(13,11),(13,20),(14,10),(14,20),(15,9),(16,10),(16,11),(17,12),(17,13),(18,8),(18,17),(18,19),(19,13),(19,14),(19,16),(20,15),(20,21),(21,9)],22)
 => [9,6,4,3]
 => [[1,2,3,4,5,6,7,8,9],[10,11,12,13,14,15],[16,17,18,19],[20,21,22]]
 => ?
 => ? = 1 + 2
([(0,6),(0,7),(1,11),(2,9),(3,9),(3,10),(4,2),(5,1),(5,10),(6,4),(7,8),(8,3),(8,5),(9,12),(10,11),(10,12),(11,13),(12,13)],14)
 => [7,5,2]
 => [[1,2,3,4,5,6,7],[8,9,10,11,12],[13,14]]
 => ?
 => ? = 1 + 2
([(0,7),(0,8),(1,10),(1,16),(2,11),(3,10),(4,12),(4,13),(5,3),(6,2),(6,16),(7,9),(8,5),(9,1),(9,6),(10,14),(11,12),(11,15),(12,17),(13,17),(14,13),(14,15),(15,17),(16,4),(16,11),(16,14)],18)
 => [8,6,4]
 => [[1,2,3,4,5,6,7,8],[9,10,11,12,13,14],[15,16,17,18]]
 => ?
 => ? = 1 + 2
Description
The row containing the largest entry of a standard tableau.
Matching statistic: St001219
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00028: Dyck paths —reverse⟶ Dyck paths
St001219: Dyck paths ⟶ ℤResult quality: 72% ●values known / values provided: 72%●distinct values known / distinct values provided: 80%
Values
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0]
 => 1 = 2 - 1
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2 = 3 - 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1 = 2 - 1
([],6)
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3 = 4 - 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 1 = 2 - 1
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 5 - 1
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
([(4,5),(4,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
([(3,4),(3,5),(3,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
([(2,3),(2,4),(2,5),(2,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(2,4),(2,5),(2,6),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(3,4),(3,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(2,5),(2,6),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(3,4),(3,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(2,3),(2,4),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(4,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(3,4),(4,5),(4,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(2,6),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(3,4),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(2,5),(5,6),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 2 - 1
([(4,6),(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
([(3,6),(4,6),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
 => ? = 3 - 1
([(3,6),(4,6),(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => ? = 4 - 1
Description
Number of simple modules S in the corresponding Nakayama algebra such that the Auslander-Reiten sequence ending at S has the property that all modules in the exact sequence are reflexive.
Matching statistic: St001231
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001231: Dyck paths ⟶ ℤResult quality: 72% ●values known / values provided: 72%●distinct values known / distinct values provided: 80%
Values
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 2 - 1
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 2 = 3 - 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([],6)
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 3 = 4 - 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 5 - 1
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(4,5),(4,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(3,4),(3,5),(3,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(2,3),(2,4),(2,5),(2,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(2,4),(2,5),(2,6),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(3,4),(3,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,5),(2,6),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,4),(3,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,3),(2,4),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(4,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,4),(4,5),(4,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,6),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,4),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(2,5),(5,6),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(4,6),(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(3,6),(4,6),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,6),(4,6),(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
Description
The number of simple modules that are non-projective and non-injective with the property that they have projective dimension equal to one and that also the Auslander-Reiten translates of the module and the inverse Auslander-Reiten translate of the module have the same projective dimension. Actually the same statistics results for algebras with at most 7 simple modules when dropping the assumption that the module has projective dimension one. The author is not sure whether this holds in general.
Matching statistic: St001234
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00030: Dyck paths —zeta map⟶ Dyck paths
St001234: Dyck paths ⟶ ℤResult quality: 72% ●values known / values provided: 72%●distinct values known / distinct values provided: 80%
Values
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1 = 2 - 1
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 2 = 3 - 1
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1 = 2 - 1
([],6)
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 3 = 4 - 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2 = 3 - 1
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 1 = 2 - 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1 = 2 - 1
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => ? = 5 - 1
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(4,5),(4,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(3,4),(3,5),(3,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(2,3),(2,4),(2,5),(2,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(2,4),(2,5),(2,6),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(3,4),(3,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,5),(2,6),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,5),(1,6),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,4),(3,5),(4,6),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,3),(2,4),(3,6),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(4,5),(5,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,4),(4,5),(4,6)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(2,6),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(1,6),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,4),(4,6),(6,5)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(2,5),(5,6),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(1,5),(5,6),(6,2),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)
 => [4,1,1,1]
 => [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,0,1,1,1,1,0,0,0,0]
 => ? = 2 - 1
([(4,6),(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
([(3,6),(4,6),(6,5)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
 => ? = 3 - 1
([(3,6),(4,6),(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,1,1,0,0,0,0,0,1,1,0,0]
 => ? = 4 - 1
Description
The number of indecomposable three dimensional modules with projective dimension one. It return zero when there are no such modules.
Matching statistic: St000689
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000689: Dyck paths ⟶ ℤResult quality: 34% ●values known / values provided: 34%●distinct values known / distinct values provided: 40%
Values
([],4)
 => [1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 1 = 2 - 1
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 2 = 3 - 1
([(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1 = 2 - 1
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1 = 2 - 1
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1 = 2 - 1
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1 = 2 - 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1 = 2 - 1
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 4 - 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 - 1
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,4),(1,5),(1,6),(5,3),(6,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(2,5),(2,6),(5,4),(6,3)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(2,3),(2,4),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,5),(1,6),(5,4),(6,2),(6,3)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 1 = 2 - 1
Description
The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. The correspondence between LNakayama algebras and Dyck paths is explained in [[St000684]]. A module M is n-rigid, if Exti(M,M)=0 for 1≤i≤n. This statistic gives the maximal n such that the minimal generator-cogenerator module A⊕D(A) of the LNakayama algebra A corresponding to a Dyck path is n-rigid. An application is to check for maximal n-orthogonal objects in the module category in the sense of [2].
Matching statistic: St001200
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 34% ●values known / values provided: 34%●distinct values known / distinct values provided: 40%
Values
([],4)
 => [1,1,1,1]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 3 = 2 + 1
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 4 = 3 + 1
([(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [3,1,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 3 = 2 + 1
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => ? = 4 + 1
([(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 3 + 1
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [5,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => ? = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,4),(1,5),(1,6),(5,3),(6,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(2,5),(2,6),(5,4),(6,3)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(2,3),(2,4),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,5),(1,6),(5,4),(6,2),(6,3)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
 => [3,2,1,1]
 => [3,3,1]
 => [1,1,1,0,1,0,0,1,0,0]
 => 3 = 2 + 1
Description
The number of simple modules in eAe with projective dimension at most 2 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA.
Matching statistic: St001491
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 32% ●values known / values provided: 32%●distinct values known / distinct values provided: 40%
Values
([],4)
 => [1,1,1,1]
 => [1,1,1]
 => 1110 => 2
([],5)
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,1,1]
 => 1110 => 2
([],6)
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 4
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,2),(1,3),(1,4)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,5),(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(1,4),(1,5),(2,3),(2,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,4),(0,5),(1,2),(1,3)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [2,1,1]
 => 10110 => ? = 2
([(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,1,1]
 => 1110 => 2
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,5),(1,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,5),(1,4),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
 => [2,2,2]
 => [2,2]
 => 1100 => 1
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1111110 => ? = 5
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 4
([(4,5),(4,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 4
([(3,4),(3,5),(3,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 4
([(2,3),(2,4),(2,5),(2,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 4
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 4
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 4
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
 => [3,1,1,1,1]
 => [1,1,1,1]
 => 11110 => ? = 3
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let An=K[x]/(xn). We associate to a nonempty subset S of an (n-1)-set the module MS, which is the direct sum of An-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 MS. 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: St001238
Mapping
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001238: Dyck paths ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 60%
Values
([],4)
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 2
([],5)
 => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 3
([(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(2,3),(2,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(1,2),(1,3),(1,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(0,1),(0,2),(0,3),(0,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 2
([],6)
 => [1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 4
([(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(3,4),(3,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(2,3),(2,4),(2,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(1,2),(1,3),(1,4),(1,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,3),(1,4),(1,5),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,4),(1,5),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(2,3),(3,4),(3,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,5),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => [2,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
([(0,5),(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,5),(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,5),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,5),(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(1,5),(2,4),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(2,5),(3,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(2,4),(2,5),(3,4),(3,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(1,5),(2,3),(2,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,2),(1,3),(1,4)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,5),(1,2),(1,3),(1,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,5),(2,3),(2,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(1,4),(1,5),(2,3),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,4),(0,5),(1,2),(1,3)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,4),(0,5),(1,2),(1,3),(1,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => [2,2,1,1]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,1,1,0,0,1,0,1,0,0,0]
 => 2
([(2,5),(3,4),(4,5)],6)
 => [3,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 2
([(0,5),(1,4),(2,3)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,5),(1,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,5),(1,4),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)
 => [2,2,2]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 1
([],7)
 => [1,1,1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 5
([(5,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 4
([(4,5),(4,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 4
([(3,4),(3,5),(3,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 4
([(2,3),(2,4),(2,5),(2,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 4
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 4
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)
 => [2,1,1,1,1,1]
 => [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]
 => ? = 4
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)
 => [3,1,1,1,1]
 => [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 3
Description
The number of simple modules S such that the Auslander-Reiten translate of S is isomorphic to the Nakayama functor applied to the second syzygy of S.
The following 210 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001186Number of simple modules with grade at least 3 in the corresponding Nakayama algebra. St001906Half of the difference between the total displacement and the number of inversions and the reflection length of a permutation. St001198The number of simple modules in the algebra eAe with projective dimension at most 1 in the corresponding Nakayama algebra A with minimal faithful projective-injective module eA. St001206The maximal dimension of an indecomposable projective eAe-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module eA. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000098The chromatic number of a graph. St001331The size of the minimal feedback vertex set. St001336The minimal number of vertices in a graph whose complement is triangle-free. St001723The differential of a graph. St001724The 2-packing differential of a graph. St000171The degree of the graph. St000261The edge connectivity of a graph. St000262The vertex connectivity of a graph. St000272The treewidth of a graph. St000310The minimal degree of a vertex of a graph. St000362The size of a minimal vertex cover of a graph. St000454The largest eigenvalue of a graph if it is integral. St000482The (zero)-forcing number of a graph. St000536The pathwidth of a graph. St000741The Colin de Verdière graph invariant. St000771The largest multiplicity of a distance Laplacian eigenvalue in a connected graph. St000772The multiplicity of the largest distance Laplacian eigenvalue in a connected graph. St000773The multiplicity of the largest Laplacian eigenvalue in a graph. St000774The maximal multiplicity of a Laplacian eigenvalue in a graph. St000776The maximal multiplicity of an eigenvalue in a graph. St000778The metric dimension of a graph. St000987The number of positive eigenvalues of the Laplacian matrix of the graph. St001119The length of a shortest maximal path in a graph. St001120The length of a longest path in a graph. St001270The bandwidth of a graph. St001277The degeneracy of a graph. St001357The maximal degree of a regular spanning subgraph of a graph. St001358The largest degree of a regular subgraph of a graph. St001391The disjunction number of a graph. St001644The dimension of a graph. St001690The length of a longest path in a graph such that after removing the paths edges, every vertex of the path has distance two from some other vertex of the path. St001702The absolute value of the determinant of the adjacency matrix of a graph. St001949The rigidity index of a graph. St001962The proper pathwidth of a graph. St000087The number of induced subgraphs. St000097The order of the largest clique of the graph. St000172The Grundy number of a graph. St000286The number of connected components of the complement of a graph. St000363The number of minimal vertex covers of a graph. St000469The distinguishing number of a graph. St000636The hull number of a graph. St000637The length of the longest cycle in a graph. St000718The largest Laplacian eigenvalue of a graph if it is integral. St000722The number of different neighbourhoods in a graph. St000822The Hadwiger number of the graph. St000926The clique-coclique number of a graph. St001029The size of the core of a graph. St001108The 2-dynamic chromatic number of a graph. St001110The 3-dynamic chromatic number of a graph. St001116The game chromatic number of a graph. St001302The number of minimally dominating sets of vertices of a graph. St001304The number of maximally independent sets of vertices of a graph. St001316The domatic number of a graph. St001330The hat guessing number of a graph. St001342The number of vertices in the center of a graph. St001366The maximal multiplicity of a degree of a vertex of a graph. St001368The number of vertices of maximal degree in a graph. St001458The rank of the adjacency matrix of a graph. St001459The number of zero columns in the nullspace of a graph. St001494The Alon-Tarsi number of a graph. St001580The acyclic chromatic number of a graph. St001581The achromatic number of a graph. St001645The pebbling number of a connected graph. St001654The monophonic hull number of a graph. St001655The general position number of a graph. St001656The monophonic position number of a graph. St001670The connected partition number of a graph. St001707The length of a longest path in a graph such that the remaining vertices can be partitioned into two sets of the same size without edges between them. St001725The harmonious chromatic number of a graph. St001746The coalition number of a graph. St001844The maximal degree of a generator of the invariant ring of the automorphism group of a graph. St001883The mutual visibility number of a graph. St001963The tree-depth of a graph. St000300The number of independent sets of vertices of a graph. St000301The number of facets of the stable set polytope of a graph. St001706The number of closed sets in a graph. St000089The absolute variation of a composition. St000377The dinv defect of an integer partition. St000934The 2-degree of an integer partition. St000008The major index of the composition. St000021The number of descents of a permutation. St000047The number of standard immaculate tableaux of a given shape. St000145The Dyson rank of a partition. St000277The number of ribbon shaped standard tableaux. St000319The spin of an integer partition. St000320The dinv adjustment of an integer partition. St000354The number of recoils of a permutation. St000381The largest part of an integer composition. St000382The first part of an integer composition. St000541The number of indices greater than or equal to 2 of a permutation such that all smaller indices appear to its right. St000619The number of cyclic descents of a permutation. St000681The Grundy value of Chomp on Ferrers diagrams. St000808The number of up steps of the associated bargraph. St000831The number of indices that are either descents or recoils. St001061The number of indices that are both descents and recoils of a permutation. St001323The independence gap of a graph. St001340The cardinality of a minimal non-edge isolating set of a graph. St001382The number of boxes in the diagram of a partition that do not lie in its Durfee square. St001384The number of boxes in the diagram of a partition that do not lie in the largest triangle it contains. St001392The largest nonnegative integer which is not a part and is smaller than the largest part of the partition. St001489The maximum of the number of descents and the number of inverse descents. St001777The number of weak descents in an integer composition. St001917The order of toric promotion on the set of labellings of a graph. St001918The degree of the cyclic sieving polynomial corresponding to an integer partition. St000093The cardinality of a maximal independent set of vertices of a graph. St000147The largest part of an integer partition. St000184The size of the centralizer of any permutation of given cycle type. St000228The size of a partition. St000258The burning number of a graph. St000273The domination number of a graph. St000287The number of connected components of a graph. St000309The number of vertices with even degree. St000315The number of isolated vertices of a graph. St000325The width of the tree associated to a permutation. St000384The maximal part of the shifted composition of an integer partition. St000459The hook length of the base cell of a partition. St000460The hook length of the last cell along the main diagonal of an integer partition. St000470The number of runs in a permutation. St000474Dyson's crank of a partition. St000477The weight of a partition according to Alladi. St000479The Ramsey number of a graph. St000531The leading coefficient of the rook polynomial of an integer partition. St000542The number of left-to-right-minima of a permutation. St000544The cop number of a graph. St000553The number of blocks of a graph. St000667The greatest common divisor of the parts of the partition. St000668The least common multiple of the parts of the partition. St000708The product of the parts of an integer partition. St000723The maximal cardinality of a set of vertices with the same neighbourhood in a graph. St000757The length of the longest weakly inreasing subsequence of parts of an integer composition. St000765The number of weak records in an integer composition. St000770The major index of an integer partition when read from bottom to top. St000775The multiplicity of the largest eigenvalue in a graph. St000784The maximum of the length and the largest part of the integer partition. St000786The maximal number of occurrences of a colour in a proper colouring of a graph. St000835The minimal difference in size when partitioning the integer partition into two subpartitions. St000870The product of the hook lengths of the diagonal cells in an integer partition. St000899The maximal number of repetitions of an integer composition. St000900The minimal number of repetitions of a part in an integer composition. St000902 The minimal number of repetitions of an integer composition. St000904The maximal number of repetitions of an integer composition. St000916The packing number of a graph. St000917The open packing number of a graph. St000918The 2-limited packing number of a graph. St000986The multiplicity of the eigenvalue zero of the adjacency matrix of the graph. St000992The alternating sum of the parts of an integer partition. St001055The Grundy value for the game of removing cells of a row in an integer partition. St001070The absolute value of the derivative of the chromatic polynomial of the graph at 1. St001102The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. St001235The global dimension of the corresponding Comp-Nakayama algebra. St001236The dominant dimension of the corresponding Comp-Nakayama algebra. St001279The sum of the parts of an integer partition that are at least two. St001286The annihilation number of a graph. St001312Number of parabolic noncrossing partitions indexed by the composition. St001315The dissociation number of a graph. St001318The number of vertices of the largest induced subforest with the same number of connected components of a graph. St001321The number of vertices of the largest induced subforest of a graph. St001322The size of a minimal independent dominating set in a graph. St001337The upper domination number of a graph. St001338The upper irredundance number of a graph. St001339The irredundance number of a graph. St001360The number of covering relations in Young's lattice below a partition. St001363The Euler characteristic of a graph according to Knill. St001373The logarithm of the number of winning configurations of the lights out game on a graph. St001389The number of partitions of the same length below the given integer partition. St001390The number of bumps occurring when Schensted-inserting the letter 1 of a permutation. St001441The number of non-empty connected induced subgraphs of a graph. St001463The number of distinct columns in the nullspace of a graph. St001527The cyclic permutation representation number of an integer partition. St001570The minimal number of edges to add to make a graph Hamiltonian. St001571The Cartan determinant of the integer partition. St001659The number of ways to place as many non-attacking rooks as possible on a Ferrers board. St001672The restrained domination number of a graph. St001675The number of parts equal to the part in the reversed composition. St001691The number of kings in a graph. St001828The Euler characteristic of a graph. St001829The common independence number of a graph. St000063The number of linear extensions of a certain poset defined for an integer partition. St000108The number of partitions contained in the given partition. St000380Half of the maximal perimeter of a rectangle fitting into the diagram of an integer partition. St000532The total number of rook placements on a Ferrers board. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St000806The semiperimeter of the associated bargraph. St001400The total number of Littlewood-Richardson tableaux of given shape. St001814The number of partitions interlacing the given partition. St001812The biclique partition number of a graph. St001674The number of vertices of the largest induced star graph in the graph. St001834The number of non-isomorphic minors of a graph. St001117The game chromatic index of a graph. St001638The book thickness of a graph. St000527The width of the poset. St000387The matching number of a graph. St001716The 1-improper chromatic number of a graph. St001792The arboricity of a graph. St000632The jump number of the poset. St000264The girth of a graph, which is not a tree. St001060The distinguishing index of a graph. St001545The second Elser number of a connected graph. St001588The number of distinct odd parts smaller than the largest even part in an integer partition. St000257The number of distinct parts of a partition that occur at least twice. St000142The number of even parts of a partition. St001092The number of distinct even parts of a partition. St001252Half the sum of the even parts of a partition. St001484The number of singletons of an integer partition. St001271The competition number of a graph.