Processing math: 100%

Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000171
Mapping
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00117: Graphs —Ore closure⟶ Graphs
St000171: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => ([],1)
 => 0
[1,2] => ([],2)
 => ([],2)
 => 0
[2,1] => ([(0,1)],2)
 => ([(0,1)],2)
 => 1
[1,2,3] => ([],3)
 => ([],3)
 => 0
[1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
[2,1,3] => ([(1,2)],3)
 => ([(1,2)],3)
 => 1
[2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2
[3,1,2] => ([(0,2),(1,2)],3)
 => ([(0,2),(1,2)],3)
 => 2
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,2,3,4] => ([],4)
 => ([],4)
 => 0
[1,2,4,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => 1
[1,3,2,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => 1
[1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
[2,1,3,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => 1
[2,1,4,3] => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 1
[2,3,1,4] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 3
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[3,1,2,4] => ([(1,3),(2,3)],4)
 => ([(1,3),(2,3)],4)
 => 2
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 2
[3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,3),(1,3),(2,3)],4)
 => 3
[4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,2,3,4,5] => ([],5)
 => ([],5)
 => 0
[1,2,3,5,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 1
[1,2,4,3,5] => ([(3,4)],5)
 => ([(3,4)],5)
 => 1
[1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 2
[1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 2
[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2
[1,3,2,4,5] => ([(3,4)],5)
 => ([(3,4)],5)
 => 1
[1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 1
[1,3,4,2,5] => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 2
[1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,4),(3,4)],5)
 => 3
[1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 2
[1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ([(2,4),(3,4)],5)
 => 2
[1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,4),(2,3),(3,4)],5)
 => 2
[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 2
[1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
Description
The degree of the graph. This is the maximal vertex degree of a graph.
Matching statistic: St001330
(load all 7 compositions to match this statistic)
Mapping
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00147: Graphs —square⟶ Graphs
St001330: Graphs ⟶ ℤResult quality: 53% ●values known / values provided: 53%●distinct values known / distinct values provided: 100%
Values
[1] => ([],1)
 => ([],1)
 => 1 = 0 + 1
[1,2] => ([],2)
 => ([],2)
 => 1 = 0 + 1
[2,1] => ([(0,1)],2)
 => ([(0,1)],2)
 => 2 = 1 + 1
[1,2,3] => ([],3)
 => ([],3)
 => 1 = 0 + 1
[1,3,2] => ([(1,2)],3)
 => ([(1,2)],3)
 => 2 = 1 + 1
[2,1,3] => ([(1,2)],3)
 => ([(1,2)],3)
 => 2 = 1 + 1
[2,3,1] => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
[3,1,2] => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => ([(0,1),(0,2),(1,2)],3)
 => 3 = 2 + 1
[1,2,3,4] => ([],4)
 => ([],4)
 => 1 = 0 + 1
[1,2,4,3] => ([(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
[1,3,2,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
[1,3,4,2] => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
[1,4,2,3] => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
[1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
[2,1,3,4] => ([(2,3)],4)
 => ([(2,3)],4)
 => 2 = 1 + 1
[2,1,4,3] => ([(0,3),(1,2)],4)
 => ([(0,3),(1,2)],4)
 => 2 = 1 + 1
[2,3,1,4] => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
[2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[3,1,2,4] => ([(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? = 2 + 1
[3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(2,3)],4)
 => 3 = 2 + 1
[3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 4 = 3 + 1
[1,2,3,4,5] => ([],5)
 => ([],5)
 => 1 = 0 + 1
[1,2,3,5,4] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2 = 1 + 1
[1,2,4,3,5] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2 = 1 + 1
[1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,3,2,4,5] => ([(3,4)],5)
 => ([(3,4)],5)
 => 2 = 1 + 1
[1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ([(1,4),(2,3)],5)
 => 2 = 1 + 1
[1,3,4,2,5] => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,3,5,4,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(3,4)],5)
 => 3 = 2 + 1
[1,4,3,5,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[1,4,5,3,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[1,5,3,2,4] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4 = 3 + 1
[2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[2,5,4,1,3] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 2 + 1
[3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,2,5,1,4] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[4,1,3,5,2] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[4,2,1,5,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 3 + 1
[4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? = 4 + 1
[1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,5,2,6,4] => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
[1,3,6,2,4,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,3,6,2,5,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,3,6,4,2,5] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,3,6,5,2,4] => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
[1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,4,2,5,6,3] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,2,6,3,5] => ([(1,5),(2,4),(3,4),(3,5)],6)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 2 + 1
[1,4,2,6,5,3] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,3,6,2,5] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
[1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
[1,4,6,3,2,5] => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
[1,5,2,3,6,4] => ([(1,5),(2,5),(3,4),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,2,4,6,3] => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
[1,5,2,6,4,3] => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
[1,5,3,2,6,4] => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 3 + 1
[1,5,4,2,6,3] => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? = 4 + 1
Description
The hat guessing number of a graph. Suppose that each vertex of a graph corresponds to a player, wearing a hat whose color is arbitrarily chosen from a set of q possible colors. Each player can see the hat colors of his neighbors, but not his own hat color. All of the players are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The hat guessing number HG(G) of a graph G is the largest integer q such that there exists a guessing strategy guaranteeing at least one correct guess for any hat assignment of q possible colors. Because it suffices that a single player guesses correctly, the hat guessing number of a graph is the maximum of the hat guessing numbers of its connected components.
Matching statistic: St001879
(load all 2 compositions to match this statistic)
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 71%
Values
[1] => [1,0]
 => [1] => ([],1)
 => ? = 0
[1,2] => [1,0,1,0]
 => [2,1] => ([],2)
 => ? = 0
[2,1] => [1,1,0,0]
 => [1,2] => ([(0,1)],2)
 => ? = 1
[1,2,3] => [1,0,1,0,1,0]
 => [3,2,1] => ([],3)
 => ? = 0
[1,3,2] => [1,0,1,1,0,0]
 => [2,3,1] => ([(1,2)],3)
 => ? = 1
[2,1,3] => [1,1,0,0,1,0]
 => [3,1,2] => ([(1,2)],3)
 => ? = 1
[2,3,1] => [1,1,0,1,0,0]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => ? = 2
[3,1,2] => [1,1,1,0,0,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[3,2,1] => [1,1,1,0,0,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 2
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => ([],4)
 => ? = 0
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => ([(2,3)],4)
 => ? = 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => ([(2,3)],4)
 => ? = 1
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ? = 2
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 2
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 2
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => ([(2,3)],4)
 => ? = 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ? = 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ? = 2
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ? = 3
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 2
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 2
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 2
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 3
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 3
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 3
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,1,3,2] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 3
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => ([],5)
 => ? = 0
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => ([(3,4)],5)
 => ? = 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => ([(3,4)],5)
 => ? = 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => ? = 2
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 2
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 2
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => ([(3,4)],5)
 => ? = 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => ? = 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => ? = 2
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
 => ? = 3
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ? = 2
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ? = 2
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 3
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 3
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => ([(3,4)],5)
 => ? = 1
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001880
(load all 2 compositions to match this statistic)
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 71%
Values
[1] => [1,0]
 => [1] => ([],1)
 => ? = 0 + 1
[1,2] => [1,0,1,0]
 => [2,1] => ([],2)
 => ? = 0 + 1
[2,1] => [1,1,0,0]
 => [1,2] => ([(0,1)],2)
 => ? = 1 + 1
[1,2,3] => [1,0,1,0,1,0]
 => [3,2,1] => ([],3)
 => ? = 0 + 1
[1,3,2] => [1,0,1,1,0,0]
 => [2,3,1] => ([(1,2)],3)
 => ? = 1 + 1
[2,1,3] => [1,1,0,0,1,0]
 => [3,1,2] => ([(1,2)],3)
 => ? = 1 + 1
[2,3,1] => [1,1,0,1,0,0]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => ? = 2 + 1
[3,1,2] => [1,1,1,0,0,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[3,2,1] => [1,1,1,0,0,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 3 = 2 + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [4,3,2,1] => ([],4)
 => ? = 0 + 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [3,4,2,1] => ([(2,3)],4)
 => ? = 1 + 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [4,2,3,1] => ([(2,3)],4)
 => ? = 1 + 1
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 2 + 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ? = 2 + 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [4,3,1,2] => ([(2,3)],4)
 => ? = 1 + 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ? = 1 + 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ? = 2 + 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ? = 3 + 1
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 2 + 1
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 2 + 1
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ? = 2 + 1
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => ? = 3 + 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 3 + 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ? = 3 + 1
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[4,1,3,2] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 4 = 3 + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => ([],5)
 => ? = 0 + 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => ([(3,4)],5)
 => ? = 1 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => ([(3,4)],5)
 => ? = 1 + 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => ? = 2 + 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 2 + 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ? = 2 + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => ([(3,4)],5)
 => ? = 1 + 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => ? = 1 + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => ? = 2 + 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
 => ? = 3 + 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ? = 2 + 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ? = 2 + 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ? = 3 + 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ? = 3 + 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ? = 3 + 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => ([(3,4)],5)
 => ? = 1 + 1
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 4 + 1
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
[6,1,4,5,3,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 5 + 1
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001232
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 86%
Values
[1] => [1,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1 = 0 + 1
[1,2] => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 0 + 1
[2,1] => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2 = 1 + 1
[1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 0 + 1
[1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ? = 1 + 1
[2,1,3] => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 1
[2,3,1] => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 2 + 1
[3,1,2] => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 2 + 1
[3,2,1] => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 2 + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ? = 1 + 1
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ? = 2 + 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => ? = 1 + 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 3 + 1
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 2 + 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 3 + 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 2 + 1
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3 + 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 3 + 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 3 + 1
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,1,3,2] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ? = 1 + 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 2 + 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => ? = 1 + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 3 + 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => ? = 2 + 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => ? = 3 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => ? = 2 + 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => ? = 3 + 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => ? = 3 + 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => ? = 3 + 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ? = 1 + 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001207
(load all 46 compositions to match this statistic)
Mapping
St001207: Permutations ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 57%
Values
[1] => ? = 0
[1,2] => 0
[2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 2
[1,2,3,4] => 0
[1,2,4,3] => 1
[1,3,2,4] => 1
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 2
[2,1,3,4] => 1
[2,1,4,3] => 1
[2,3,1,4] => 2
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 3
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 2
[3,2,4,1] => 3
[3,4,1,2] => 3
[3,4,2,1] => 3
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 3
[4,3,2,1] => 3
[1,2,3,4,5] => ? = 0
[1,2,3,5,4] => ? = 1
[1,2,4,3,5] => ? = 1
[1,2,4,5,3] => ? = 2
[1,2,5,3,4] => ? = 2
[1,2,5,4,3] => ? = 2
[1,3,2,4,5] => ? = 1
[1,3,2,5,4] => ? = 1
[1,3,4,2,5] => ? = 2
[1,3,4,5,2] => ? = 3
[1,3,5,2,4] => ? = 2
[1,3,5,4,2] => ? = 3
[1,4,2,3,5] => ? = 2
[1,4,2,5,3] => ? = 2
[1,4,3,2,5] => ? = 2
[1,4,3,5,2] => ? = 3
[1,4,5,2,3] => ? = 3
[1,4,5,3,2] => ? = 3
[1,5,2,3,4] => ? = 3
[1,5,2,4,3] => ? = 3
[1,5,3,2,4] => ? = 3
[1,5,3,4,2] => ? = 3
[1,5,4,2,3] => ? = 3
[1,5,4,3,2] => ? = 3
[2,1,3,4,5] => ? = 1
[2,1,3,5,4] => ? = 1
[2,1,4,3,5] => ? = 1
[2,1,4,5,3] => ? = 2
[2,1,5,3,4] => ? = 2
[2,1,5,4,3] => ? = 2
[2,3,1,4,5] => ? = 2
[2,3,1,5,4] => ? = 2
[2,3,4,1,5] => ? = 3
[2,3,4,5,1] => ? = 4
[2,3,5,1,4] => ? = 3
[2,3,5,4,1] => ? = 4
[2,4,1,3,5] => ? = 2
[2,4,1,5,3] => ? = 2
[2,4,3,1,5] => ? = 3
[2,4,3,5,1] => ? = 4
[2,4,5,1,3] => ? = 4
[2,4,5,3,1] => ? = 4
[2,5,1,3,4] => ? = 3
[2,5,1,4,3] => ? = 3
[2,5,3,1,4] => ? = 3
[2,5,3,4,1] => ? = 4
[2,5,4,1,3] => ? = 4
[2,5,4,3,1] => ? = 4
[3,1,2,4,5] => ? = 2
Description
The Lowey length of the algebra A/T when T is the 1-tilting module corresponding to the permutation in the Auslander algebra of K[x]/(xn).