Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000264
Mapping
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00156: Graphs —line graph⟶ Graphs
Mp00111: Graphs —complement⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 6
[3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => 6
[3,5,1,4,2] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 5
[3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[3,5,4,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[4,2,5,1,3] => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 5
[4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[4,3,5,1,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 6
[4,5,1,3,2] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[4,5,2,1,3] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => 6
[5,2,4,1,3] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[5,3,1,4,2] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => 6
[1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 6
[1,4,5,6,3,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => 6
[1,4,6,2,5,3] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 5
[1,4,6,3,5,2] => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[1,4,6,5,2,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[1,5,3,6,2,4] => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
 => 5
[1,5,3,6,4,2] => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[1,5,4,6,2,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)
 => 6
[1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[1,5,6,3,2,4] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => 5
[1,6,3,4,5,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => 6
[1,6,3,5,2,4] => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[1,6,4,2,5,3] => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)
 => 5
[1,6,5,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => ([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)
 => 6
[2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
 => ([],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3
[2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[2,1,4,6,5,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6)
 => ([(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[2,1,5,4,6,3] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 3
[2,1,5,6,4,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 3
[2,1,6,3,5,4] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[2,1,6,4,3,5] => ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[2,1,6,4,5,3] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 3
[2,1,6,5,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 3
[2,1,6,5,4,3] => ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)
 => 3
[2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6)
 => ([(0,3),(1,2)],4)
 => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[2,3,1,6,5,4] => ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)
 => ([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 4
[2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => 4
[2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[2,3,6,1,5,4] => ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St001626
(load all 2 compositions to match this statistic)
Mapping
Mp00065: Permutations —permutation poset⟶ Posets
Mp00282: Posets —Dedekind-MacNeille completion⟶ Lattices
St001626: Lattices ⟶ ℤResult quality: 7% ●values known / values provided: 7%●distinct values known / distinct values provided: 50%
Values
[3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => 5 = 6 - 1
[3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[3,5,1,4,2] => ([(0,3),(0,4),(1,2),(1,4)],5)
 => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[3,5,2,4,1] => ([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[3,5,4,1,2] => ([(0,4),(1,2),(1,3)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => 4 = 5 - 1
[4,2,5,1,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 5 - 1
[4,2,5,3,1] => ([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => 4 = 5 - 1
[4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => 5 = 6 - 1
[4,5,1,3,2] => ([(0,4),(1,2),(1,3)],5)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => 4 = 5 - 1
[4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => 4 = 5 - 1
[5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[5,3,1,4,2] => ([(1,4),(2,3),(2,4)],5)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[5,4,1,2,3] => ([(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[1,4,5,6,2,3] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => 5 = 6 - 1
[1,4,5,6,3,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[1,4,6,2,5,3] => ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
 => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[1,4,6,3,5,2] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[1,4,6,5,2,3] => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => 4 = 5 - 1
[1,5,3,6,2,4] => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 5 - 1
[1,5,3,6,4,2] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[1,5,4,6,2,3] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => 4 = 5 - 1
[1,5,6,2,3,4] => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => 5 = 6 - 1
[1,5,6,2,4,3] => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => 4 = 5 - 1
[1,5,6,3,2,4] => ([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => 4 = 5 - 1
[1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[1,6,3,5,2,4] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[1,6,4,2,5,3] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[1,6,5,2,3,4] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
 => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,9),(6,9),(8,1),(8,2),(9,3),(9,4)],10)
 => ? = 3 - 1
[2,1,4,6,3,5] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ? = 3 - 1
[2,1,4,6,5,3] => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],9)
 => ? = 3 - 1
[2,1,5,3,6,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,8),(4,8),(5,1),(5,6),(6,7),(8,2),(8,5)],9)
 => ? = 3 - 1
[2,1,5,4,6,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,8),(6,7),(8,1),(8,2),(8,3)],9)
 => ? = 3 - 1
[2,1,5,6,3,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)
 => ([(0,3),(0,4),(1,7),(2,7),(3,8),(4,8),(5,2),(6,1),(8,5),(8,6)],9)
 => ? = 3 - 1
[2,1,5,6,4,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,3),(7,6)],9)
 => ? = 3 - 1
[2,1,6,3,5,4] => ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
 => ([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(6,2),(7,3),(7,6)],9)
 => ? = 3 - 1
[2,1,6,4,3,5] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,8),(6,7),(8,1),(8,2),(8,3)],9)
 => ? = 3 - 1
[2,1,6,4,5,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,3),(7,6)],9)
 => ? = 3 - 1
[2,1,6,5,3,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,5),(1,8),(2,8),(3,8),(4,7),(5,7),(6,1),(7,2),(7,3),(7,6)],9)
 => ? = 3 - 1
[2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
 => ([(0,5),(0,6),(1,8),(2,8),(3,8),(4,8),(5,7),(6,7),(7,1),(7,2),(7,3),(7,4)],9)
 => ? = 3 - 1
[2,3,1,5,6,4] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(8,2),(8,5)],9)
 => ? = 4 - 1
[2,3,1,6,4,5] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
 => ([(0,4),(0,6),(1,8),(2,7),(3,7),(4,8),(5,3),(6,1),(8,2),(8,5)],9)
 => ? = 4 - 1
[2,3,1,6,5,4] => ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
 => ([(0,5),(0,6),(1,7),(2,8),(3,8),(4,8),(5,7),(6,1),(7,2),(7,3),(7,4)],9)
 => ? = 4 - 1
[2,3,5,1,6,4] => ([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)
 => ([(0,3),(0,5),(1,7),(2,6),(3,8),(4,2),(4,8),(5,4),(6,7),(8,1),(8,6)],9)
 => ? = 4 - 1
[2,3,5,6,1,4] => ([(0,5),(1,4),(3,2),(4,3),(4,5)],6)
 => ([(0,2),(0,5),(1,7),(2,6),(3,1),(4,3),(4,6),(5,4),(6,7)],8)
 => ? = 4 - 1
[2,3,5,6,4,1] => ([(1,5),(4,3),(5,2),(5,4)],6)
 => ([(0,3),(0,5),(1,7),(2,7),(3,7),(4,2),(5,6),(6,1),(6,4)],8)
 => ? = 4 - 1
[2,3,6,1,4,5] => ([(0,5),(1,4),(4,2),(4,5),(5,3)],6)
 => ([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(4,7),(5,4),(7,1)],8)
 => ? = 4 - 1
[2,3,6,1,5,4] => ([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)
 => ([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,1),(5,7),(6,5),(7,2),(7,3)],9)
 => ? = 4 - 1
[2,3,6,4,1,5] => ([(0,5),(1,4),(3,5),(4,2),(4,3)],6)
 => ([(0,3),(0,4),(1,7),(2,6),(3,6),(4,5),(5,1),(5,2),(6,7)],8)
 => ? = 4 - 1
[2,3,6,4,5,1] => ([(1,5),(4,3),(5,2),(5,4)],6)
 => ([(0,3),(0,5),(1,7),(2,7),(3,7),(4,2),(5,6),(6,1),(6,4)],8)
 => ? = 4 - 1
[2,3,6,5,1,4] => ([(0,5),(1,4),(4,2),(4,3),(4,5)],6)
 => ([(0,3),(0,4),(1,7),(2,7),(3,6),(4,5),(5,1),(5,2),(5,6),(6,7)],8)
 => ? = 4 - 1
[2,4,1,3,6,5] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,8),(8,2),(8,3)],9)
 => ? = 3 - 1
[2,4,1,5,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
 => ([(0,4),(0,5),(1,8),(2,6),(3,6),(4,7),(5,1),(5,7),(7,2),(7,8),(8,3)],9)
 => ? = 4 - 1
[2,4,1,6,3,5] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
 => ([(0,4),(0,5),(1,7),(2,9),(3,6),(4,8),(5,2),(5,8),(6,7),(8,3),(8,9),(9,1),(9,6)],10)
 => ? = 3 - 1
[2,4,1,6,5,3] => ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)
 => ([(0,5),(0,6),(1,8),(2,9),(3,9),(4,9),(5,7),(6,1),(6,7),(7,4),(7,8),(8,2),(8,3)],10)
 => ? = 3 - 1
[2,4,3,1,6,5] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,8),(2,8),(3,7),(4,7),(5,8),(6,1),(6,2),(8,3),(8,4)],9)
 => ? = 3 - 1
[2,4,3,6,1,5] => ([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,7),(2,8),(3,8),(4,6),(5,2),(5,3),(6,7),(8,1),(8,6)],9)
 => ? = 3 - 1
[2,4,3,6,5,1] => ([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
 => ([(0,5),(0,6),(1,7),(2,7),(3,8),(4,8),(5,8),(6,1),(6,2),(7,3),(7,4)],9)
 => ? = 3 - 1
[2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
 => ([(0,3),(0,5),(1,7),(2,6),(3,8),(4,2),(5,4),(5,8),(6,7),(8,1),(8,6)],9)
 => ? = 4 - 1
[2,4,5,3,6,1] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)
 => ? = 4 - 1
[2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(4,1),(5,3),(5,6),(6,7)],8)
 => ? = 4 - 1
[2,4,6,1,3,5] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
 => ? = 3 - 1
[2,4,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)
 => ([(0,3),(0,5),(1,8),(2,8),(3,7),(4,2),(4,6),(5,4),(5,7),(6,8),(7,1),(7,6)],9)
 => ? = 3 - 1
[2,4,6,3,1,5] => ([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)
 => ([(0,3),(0,5),(1,7),(2,6),(3,7),(4,2),(4,7),(5,1),(5,4),(7,6)],8)
 => ? = 3 - 1
[2,5,1,3,6,4] => ([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)
 => ([(0,3),(0,4),(1,6),(2,5),(3,7),(4,2),(4,7),(5,6),(7,1),(7,5)],8)
 => ? = 3 - 1
[2,5,1,4,6,3] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,3),(5,8),(6,7),(8,1),(8,2)],9)
 => ? = 3 - 1
[2,5,1,6,3,4] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)
 => ([(0,3),(0,5),(1,8),(2,7),(3,6),(4,2),(5,1),(5,6),(6,4),(6,8),(8,7)],9)
 => ? = 3 - 1
[2,5,1,6,4,3] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
 => ([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,3),(5,7),(6,8),(7,1),(7,2),(7,6)],9)
 => ? = 3 - 1
[2,5,3,1,6,4] => ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)
 => ([(0,4),(0,5),(1,7),(2,8),(3,6),(4,8),(5,2),(5,3),(6,7),(8,1),(8,6)],9)
 => ? = 3 - 1
[2,5,3,4,6,1] => ([(1,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,1),(5,4),(6,7)],8)
 => ? = 4 - 1
[2,5,3,6,1,4] => ([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)
 => ([(0,3),(0,4),(1,5),(2,5),(2,6),(3,6),(4,1),(4,2),(5,7),(6,7)],8)
 => ? = 3 - 1
[2,5,4,1,6,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)
 => ([(0,4),(0,5),(1,8),(2,8),(3,6),(4,7),(5,1),(5,2),(5,7),(7,3),(7,8),(8,6)],9)
 => ? = 3 - 1
[2,5,6,1,3,4] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6)
 => ([(0,3),(0,5),(1,6),(2,6),(3,7),(4,2),(5,4),(5,7),(7,1)],8)
 => ? = 3 - 1
[2,6,1,3,5,4] => ([(0,5),(1,2),(1,5),(5,3),(5,4)],6)
 => ([(0,4),(0,5),(1,7),(2,7),(3,7),(4,6),(5,1),(5,6),(6,2),(6,3)],8)
 => ? = 3 - 1
[2,6,1,4,3,5] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,8),(5,1),(5,8),(6,7),(8,2),(8,3)],9)
 => ? = 3 - 1
[2,6,1,4,5,3] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,3),(7,5)],9)
 => ? = 3 - 1
[2,6,1,5,3,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
 => ([(0,4),(0,6),(1,8),(2,8),(3,8),(4,7),(5,2),(6,1),(6,7),(7,3),(7,5)],9)
 => ? = 3 - 1
[2,6,3,1,4,5] => ([(0,5),(1,2),(1,3),(3,5),(5,4)],6)
 => ([(0,4),(0,5),(1,7),(2,6),(3,6),(4,7),(5,1),(5,3),(7,2)],8)
 => ? = 4 - 1
[3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => 5 = 6 - 1
[3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[3,5,1,4,2,6] => ([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[3,5,2,4,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[3,5,4,1,2,6] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => 4 = 5 - 1
[4,2,5,1,3,6] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)
 => 4 = 5 - 1
[4,2,5,3,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => 4 = 5 - 1
[4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => 5 = 6 - 1
[4,5,1,3,2,6] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => 4 = 5 - 1
[4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(5,6)],7)
 => 4 = 5 - 1
[5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[5,2,4,1,3,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[5,3,1,4,2,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[1,4,5,6,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)
 => 5 = 6 - 1
[1,4,5,6,3,2,7] => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => ([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)
 => 5 = 6 - 1
[1,4,6,2,5,3,7] => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[1,4,6,3,5,2,7] => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)
 => 4 = 5 - 1
[1,4,6,5,2,3,7] => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => ([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)
 => 4 = 5 - 1
Description
The number of maximal proper sublattices of a lattice.
Matching statistic: St001232
Mapping
Mp00159: Permutations —Demazure product with inverse⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 25%
Values
[3,4,5,1,2] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 6
[3,4,5,2,1] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 6
[3,5,1,4,2] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[3,5,2,4,1] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[3,5,4,1,2] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[4,2,5,1,3] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[4,2,5,3,1] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[4,3,5,1,2] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[4,5,1,2,3] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 6
[4,5,1,3,2] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[4,5,2,1,3] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[5,2,3,4,1] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 6
[5,2,4,1,3] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[5,3,1,4,2] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 5
[5,4,1,2,3] => [5,4,3,2,1] => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => ? = 6
[1,4,5,6,2,3] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 6
[1,4,5,6,3,2] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 6
[1,4,6,2,5,3] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,4,6,3,5,2] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,4,6,5,2,3] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,5,3,6,2,4] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,5,3,6,4,2] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,5,4,6,2,3] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,5,6,2,3,4] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 6
[1,5,6,2,4,3] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,5,6,3,2,4] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,6,3,4,5,2] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 6
[1,6,3,5,2,4] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,6,4,2,5,3] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 5
[1,6,5,2,3,4] => [1,6,5,4,3,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 6
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,4,6,3,5] => [2,1,5,6,3,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,4,6,5,3] => [2,1,6,5,4,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,5,3,6,4] => [2,1,6,4,5,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 3
[2,1,5,4,6,3] => [2,1,6,4,5,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 3
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,5,6,4,3] => [2,1,6,5,4,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,6,3,5,4] => [2,1,6,4,5,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 3
[2,1,6,4,3,5] => [2,1,6,5,4,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,6,4,5,3] => [2,1,6,5,4,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,6,5,3,4] => [2,1,6,5,4,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,3,1,5,6,4] => [3,2,1,6,5,4] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,1,6,4,5] => [3,2,1,6,5,4] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,1,6,5,4] => [3,2,1,6,5,4] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,5,1,6,4] => [4,2,6,1,5,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,5,6,1,4] => [5,2,6,4,1,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,5,6,4,1] => [6,2,5,4,3,1] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,6,1,4,5] => [4,2,6,1,5,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,6,1,5,4] => [4,2,6,1,5,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,6,4,1,5] => [5,2,6,4,1,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,6,4,5,1] => [6,2,5,4,3,1] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,3,6,5,1,4] => [5,2,6,4,1,3] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,4,1,3,6,5] => [3,4,1,2,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,1,5,6,3] => [3,6,1,4,5,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,4,1,6,3,5] => [3,5,1,6,2,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,1,6,5,3] => [3,6,1,5,4,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,3,1,6,5] => [4,3,2,1,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,3,6,1,5] => [5,3,2,6,1,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,3,6,5,1] => [6,3,2,5,4,1] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,5,1,6,3] => [4,6,3,1,5,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,4,5,3,6,1] => [6,4,3,2,5,1] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,4,5,6,1,3] => [5,6,3,4,1,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 4
[2,4,6,1,3,5] => [4,5,6,1,2,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,6,1,5,3] => [4,6,5,1,3,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,4,6,3,1,5] => [5,4,6,2,1,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,5,1,3,6,4] => [3,6,1,4,5,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 3
[2,5,1,4,6,3] => [3,6,1,4,5,2] => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => ? = 3
[2,5,1,6,3,4] => [3,6,1,5,4,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,5,1,6,4,3] => [3,6,1,5,4,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,5,6,1,3,4] => [4,6,5,1,3,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,6,1,4,3,5] => [3,6,1,5,4,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,6,1,4,5,3] => [3,6,1,5,4,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,6,1,5,3,4] => [3,6,1,5,4,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[2,6,4,1,3,5] => [4,6,5,1,3,2] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[3,4,1,2,6,5] => [4,3,2,1,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[3,4,1,6,2,5] => [5,3,2,6,1,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[3,4,1,6,5,2] => [6,3,2,5,4,1] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[3,4,2,1,6,5] => [4,3,2,1,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[3,4,2,6,1,5] => [5,3,2,6,1,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[3,4,6,1,2,5] => [5,4,6,2,1,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,2,1,3,6,5] => [4,3,2,1,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,2,1,6,3,5] => [5,3,2,6,1,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,2,1,6,5,3] => [6,3,2,5,4,1] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,2,3,1,6,5] => [4,3,2,1,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,2,3,6,1,5] => [5,3,2,6,1,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,2,6,1,3,5] => [5,4,6,2,1,3] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,3,1,2,6,5] => [4,3,2,1,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,3,1,6,2,5] => [5,3,2,6,1,4] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[5,2,1,6,3,4] => [6,3,2,5,4,1] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[6,2,1,4,3,5] => [6,3,2,5,4,1] => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.