Your data matches 18 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000981
(load all 9 compositions to match this statistic)
Mapping
St000981: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => 4
[1,1,0,0]
 => 2
[1,0,1,0,1,0]
 => 6
[1,0,1,1,0,0]
 => 3
[1,1,0,0,1,0]
 => 3
[1,1,0,1,0,0]
 => 4
[1,1,1,0,0,0]
 => 2
[1,0,1,0,1,0,1,0]
 => 8
[1,0,1,0,1,1,0,0]
 => 5
[1,0,1,1,0,0,1,0]
 => 3
[1,0,1,1,0,1,0,0]
 => 4
[1,0,1,1,1,0,0,0]
 => 3
[1,1,0,0,1,0,1,0]
 => 5
[1,1,0,0,1,1,0,0]
 => 2
[1,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,0,1,0,0]
 => 6
[1,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,0,0,1,0]
 => 3
[1,1,1,0,0,1,0,0]
 => 3
[1,1,1,0,1,0,0,0]
 => 4
[1,1,1,1,0,0,0,0]
 => 2
[1,0,1,0,1,0,1,0,1,0]
 => 10
[1,0,1,0,1,0,1,1,0,0]
 => 7
[1,0,1,0,1,1,0,0,1,0]
 => 5
[1,0,1,0,1,1,0,1,0,0]
 => 5
[1,0,1,0,1,1,1,0,0,0]
 => 5
[1,0,1,1,0,0,1,0,1,0]
 => 5
[1,0,1,1,0,0,1,1,0,0]
 => 3
[1,0,1,1,0,1,0,0,1,0]
 => 4
[1,0,1,1,0,1,0,1,0,0]
 => 6
[1,0,1,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,0,0,0,1,0]
 => 3
[1,0,1,1,1,0,0,1,0,0]
 => 3
[1,0,1,1,1,0,1,0,0,0]
 => 4
[1,0,1,1,1,1,0,0,0,0]
 => 3
[1,1,0,0,1,0,1,0,1,0]
 => 7
[1,1,0,0,1,0,1,1,0,0]
 => 4
[1,1,0,0,1,1,0,0,1,0]
 => 3
[1,1,0,0,1,1,0,1,0,0]
 => 4
[1,1,0,0,1,1,1,0,0,0]
 => 2
[1,1,0,1,0,0,1,0,1,0]
 => 5
[1,1,0,1,0,0,1,1,0,0]
 => 4
[1,1,0,1,0,1,0,0,1,0]
 => 6
[1,1,0,1,0,1,0,1,0,0]
 => 8
[1,1,0,1,0,1,1,0,0,0]
 => 5
[1,1,0,1,1,0,0,0,1,0]
 => 3
[1,1,0,1,1,0,0,1,0,0]
 => 3
[1,1,0,1,1,0,1,0,0,0]
 => 4
[1,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => 5
Description
The length of the longest zigzag subpath. This is the length of the longest consecutive subpath that is a zigzag of the form $010...$ or of the form $101...$.
Matching statistic: St000777
(load all 12 compositions to match this statistic)
Mapping
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 42%
Values
[1,0,1,0]
 => [1,2] => [2] => ([],2)
 => ? ∊ {2,4}
[1,1,0,0]
 => [2,1] => [2] => ([],2)
 => ? ∊ {2,4}
[1,0,1,0,1,0]
 => [1,2,3] => [3] => ([],3)
 => ? ∊ {2,3,4,6}
[1,0,1,1,0,0]
 => [1,3,2] => [1,2] => ([(1,2)],3)
 => ? ∊ {2,3,4,6}
[1,1,0,0,1,0]
 => [2,1,3] => [3] => ([],3)
 => ? ∊ {2,3,4,6}
[1,1,0,1,0,0]
 => [2,3,1] => [3] => ([],3)
 => ? ∊ {2,3,4,6}
[1,1,1,0,0,0]
 => [3,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 3
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [4] => ([],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [1,3] => ([(2,3)],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [1,3] => ([(2,3)],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [4] => ([],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [4] => ([],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [4] => ([],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,1,0,1,1,0,0,0]
 => [2,4,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,4,5,5,6,8}
[1,1,1,0,1,0,0,0]
 => [3,4,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[1,1,1,1,0,0,0,0]
 => [4,3,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [5] => ([],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,4] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,4] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [1,4] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [5] => ([],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [5] => ([],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [5] => ([],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [5] => ([],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,3,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,1,1,0,1,0,0,0,1,0]
 => [3,4,2,1,5] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,0,0,1,0,0]
 => [3,4,2,5,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,0,1,0,0,0]
 => [3,4,5,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
[1,1,1,0,1,1,0,0,0,0]
 => [3,5,4,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,8,10}
[1,1,1,1,0,0,1,0,0,0]
 => [4,3,5,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,1,1,1,0,1,0,0,0,0]
 => [4,5,3,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6] => [6] => ([],6)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,4,6,5] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,2,3,5,6,4] => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,2,3,6,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [2,4] => ([(3,5),(4,5)],6)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,2,4,3,6,5] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,2,4,6,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,2,5,6,4,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,2,6,5,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,3,2,6,5,4] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,3,4,6,5,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
[1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,3,5,6,4,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,3,6,5,4,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,4,3,6,5,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,4,5,6,3,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,4,6,5,3,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 6
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,5,4,6,3,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,5,6,4,3,2] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,6,5,4,3,2] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 4
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3,6,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [2,1,4,6,5,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [2,1,5,6,4,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,1,6,5,4,3] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [2,3,1,6,5,4] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,3,4,6,5,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 3
[1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,3,5,6,4,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 3
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,3,6,5,4,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,4,3,6,5,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,4,5,6,3,1] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,4,6,5,3,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,5,4,6,3,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,5,6,4,3,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,6,5,4,3,1] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,2,1,6,5,4] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,2,4,6,5,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
[1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,5,6,4,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 5
Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
Matching statistic: St001875
(load all 7 compositions to match this statistic)
Mapping
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001875: Lattices ⟶ ℤResult quality: 37% ●values known / values provided: 37%●distinct values known / distinct values provided: 42%
Values
[1,0,1,0]
 => [2,1] => ([],2)
 => ([],1)
 => ? ∊ {2,4}
[1,1,0,0]
 => [1,2] => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,4}
[1,0,1,0,1,0]
 => [3,2,1] => ([],3)
 => ([],1)
 => ? ∊ {2,3,4,6}
[1,0,1,1,0,0]
 => [2,3,1] => ([(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,3,4,6}
[1,1,0,0,1,0]
 => [3,1,2] => ([(1,2)],3)
 => ([(0,1)],2)
 => ? ∊ {2,3,4,6}
[1,1,0,1,0,0]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => ([],1)
 => ? ∊ {2,3,4,6}
[1,1,1,0,0,0]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,0,1,0]
 => [4,3,2,1] => ([],4)
 => ([],1)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,0,1,0,1,1,0,0]
 => [3,4,2,1] => ([(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,0,1,1,0,0,1,0]
 => [4,2,3,1] => ([(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,0,1,1,0,1,0,0]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,0,1,1,1,0,0,0]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,0,1,0,1,0]
 => [4,3,1,2] => ([(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,1,0,0,1,1,0,0]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,1,0,0,1,0]
 => [4,2,1,3] => ([(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,1,0,1,0,1,0,0]
 => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => ([],1)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,1,0,1,1,0,0,0]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,1,1,0,0,0,1,0]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,1,0,0]
 => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => ([(0,1)],2)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,1,1,0,1,0,0,0]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => ([],1)
 => ? ∊ {2,2,3,3,4,4,5,5,6,8}
[1,1,1,1,0,0,0,0]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1] => ([],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,0,1,1,0,0]
 => [4,5,3,2,1] => ([(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,0,1,0]
 => [5,3,4,2,1] => ([(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,1,0,0]
 => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,1,0,0,0]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,3,1] => ([(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,1,0,0]
 => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,1,0,0,0]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,0,1,0]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,1,0,0,1,0,0]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,1,0,0,0]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,2] => ([(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,1,0,0]
 => [4,5,3,1,2] => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,0,1,1,0,0,1,0]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,0,1,1,0,1,0,0]
 => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,1,0,0,0]
 => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
[1,1,0,1,0,0,1,0,1,0]
 => [5,4,2,1,3] => ([(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,1,0,0]
 => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,0,1,0]
 => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,0,1,0]
 => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,1,0,0]
 => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,1,0,0,0]
 => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [5,4,1,2,3] => ([(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,0,1,1,0,0]
 => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
[1,1,1,0,0,1,0,0,1,0]
 => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,1,0,0,0]
 => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,1,0,1,0,0,0,1,0]
 => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,0,0,1,0,0]
 => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,0,1,0,0,0]
 => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,1,0,0,0,0]
 => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,1,0,0,0,0,1,0]
 => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,1,0,0,1,0,0,0]
 => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,1,0,1,0,0,0,0]
 => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [6,5,4,3,2,1] => ([],6)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [5,6,4,3,2,1] => ([(4,5)],6)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [6,4,5,3,2,1] => ([(4,5)],6)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [5,4,6,3,2,1] => ([(3,5),(4,5)],6)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [4,5,6,3,2,1] => ([(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [6,5,3,4,2,1] => ([(4,5)],6)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [5,6,3,4,2,1] => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [6,4,3,5,2,1] => ([(3,5),(4,5)],6)
 => ([],1)
 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [6,3,4,5,2,1] => ([(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [5,6,4,2,3,1] => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [6,4,5,2,3,1] => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [6,5,2,3,4,1] => ([(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [5,6,4,3,1,2] => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [6,4,5,3,1,2] => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [6,5,3,4,1,2] => ([(2,5),(3,4)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,1,0,0,1,1,1,0,0,0]
 => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,1,1,0,0,1,1,0,0,0]
 => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 3
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [6,5,4,1,2,3] => ([(3,4),(4,5)],6)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,0,1,0,1,1,0,0]
 => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6)
 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
 => 4
Description
The number of simple modules with projective dimension at most 1.
Matching statistic: St000264
(load all 5 compositions to match this statistic)
Mapping
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 35%●distinct values known / distinct values provided: 17%
Values
[1,0,1,0]
 => [1,2] => [1,2] => ([],2)
 => ? ∊ {2,4}
[1,1,0,0]
 => [2,1] => [1,2] => ([],2)
 => ? ∊ {2,4}
[1,0,1,0,1,0]
 => [1,2,3] => [1,2,3] => ([],3)
 => ? ∊ {2,3,3,4,6}
[1,0,1,1,0,0]
 => [1,3,2] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {2,3,3,4,6}
[1,1,0,0,1,0]
 => [2,1,3] => [1,3,2] => ([(1,2)],3)
 => ? ∊ {2,3,3,4,6}
[1,1,0,1,0,0]
 => [2,3,1] => [1,2,3] => ([],3)
 => ? ∊ {2,3,3,4,6}
[1,1,1,0,0,0]
 => [3,2,1] => [1,2,3] => ([],3)
 => ? ∊ {2,3,3,4,6}
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,2,3,4] => ([],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [1,3,2,4] => ([(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,1,0,0]
 => [2,3,4,1] => [1,2,3,4] => ([],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,1,0,0,0]
 => [2,4,3,1] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,1,0,0]
 => [3,2,4,1] => [1,2,4,3] => ([(2,3)],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,1,0,0,0]
 => [4,2,3,1] => [1,2,3,4] => ([],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,1,0,0,0,0]
 => [4,3,2,1] => [1,2,3,4] => ([],4)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [1,2,3,4,5] => ([],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,3,4,2,5] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,1,0,0,0]
 => [1,5,3,4,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [1,4,2,3,5] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => [1,2,3,4,5] => ([],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => [1,2,3,5,4] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => [1,2,4,3,5] => ([(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,1,0,0,0]
 => [2,5,3,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [1,5,2,4,3] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,0,0,0,1,0]
 => [4,2,3,1,5] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,5,3,4,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,6,3,5,4,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,5,4,3,2,6] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,6,4,3,5,2] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [2,1,3,5,6,4] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [2,1,4,5,3,6] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,0,0,1,1,0,1,0,1,0,0]
 => [2,1,4,5,6,3] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [2,1,4,6,5,3] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
[1,1,0,1,0,0,1,0,1,0,1,0]
 => [2,3,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,0,1,0,0,1,0,1,1,0,0]
 => [2,3,1,4,6,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [2,3,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [2,3,4,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [2,3,5,4,1,6] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [2,4,3,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 3
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [2,4,3,1,6,5] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [2,4,3,5,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [2,5,3,4,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,6,3,5,4,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [2,5,4,3,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,6,4,3,5,1] => [1,2,6,3,5,4] => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [3,2,1,4,5,6] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,1,0,0,0,1,0,1,1,0,0]
 => [3,2,1,4,6,5] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 4
[1,1,1,0,0,0,1,1,0,1,0,0]
 => [3,2,1,5,6,4] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,1,0,0,1,0,0,1,0,1,0]
 => [3,2,4,1,5,6] => [1,5,6,2,4,3] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 3
[1,1,1,0,0,1,0,0,1,1,0,0]
 => [3,2,4,1,6,5] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,1,0,0,1,0,1,0,0,1,0]
 => [3,2,4,5,1,6] => [1,6,2,4,5,3] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,1,0,0,1,1,0,0,0,1,0]
 => [3,2,5,4,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,1,0,1,0,0,0,1,0,1,0]
 => [4,2,3,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,1,0,1,0,0,1,0,0,1,0]
 => [4,2,3,5,1,6] => [1,6,2,3,5,4] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,2,4,3,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [4,3,2,1,5,6] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [4,3,2,5,1,6] => [1,6,2,5,3,4] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,3,2,5,6,1] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 4
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [5,3,2,4,1,6] => [1,6,2,4,3,5] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,2,6,4,5,3,7] => [1,2,6,3,7,4,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,2,7,4,6,5,3] => [1,2,7,3,4,6,5] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,2,6,5,4,3,7] => [1,2,6,3,7,4,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,2,7,5,4,6,3] => [1,2,7,3,4,6,5] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
 => [1,3,6,4,5,2,7] => [1,3,6,2,7,4,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,3,7,4,6,5,2] => [1,3,7,2,4,6,5] => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,3,6,5,4,2,7] => [1,3,6,2,7,4,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,3,7,5,4,6,2] => [1,3,7,2,4,6,5] => ([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)
 => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
 => [1,4,3,2,6,7,5] => [1,4,2,6,7,3,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
 => [1,4,3,5,2,6,7] => [1,4,2,6,7,3,5] => ([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)
 => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
 => [1,4,3,6,5,2,7] => [1,4,2,7,3,6,5] => ([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)
 => 3
Description
The girth of a graph, which is not a tree. This is the length of the shortest cycle in the graph.
Matching statistic: St001880
(load all 14 compositions to match this statistic)
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00192: Skew partitions —dominating sublattice⟶ Lattices
Mp00193: Lattices —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 42%
Values
[1,0,1,0]
 => [[1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,4}
[1,1,0,0]
 => [[2],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,4}
[1,0,1,0,1,0]
 => [[1,1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,3,3,4,6}
[1,0,1,1,0,0]
 => [[2,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,3,3,4,6}
[1,1,0,0,1,0]
 => [[2,2],[1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,3,3,4,6}
[1,1,0,1,0,0]
 => [[3],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,3,3,4,6}
[1,1,1,0,0,0]
 => [[2,2],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,3,3,4,6}
[1,0,1,0,1,0,1,0]
 => [[1,1,1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,0,1,1,0,0]
 => [[2,1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,1,0,0]
 => [[3,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,1,0,0,0]
 => [[2,2,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,1,0,0]
 => [[4],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,1,0,0,0]
 => [[3,3],[1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,1,0,0]
 => [[3,2],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,1,0,0,0]
 => [[2,2,2],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,1,0,0,0,0]
 => [[3,3],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,3,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,0,1,0,1,0,1,0]
 => [[1,1,1,1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,0,1,1,0,0]
 => [[2,1,1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,1,0,0]
 => [[3,1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,1,0,0,0]
 => [[2,2,1,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,1,0,0]
 => [[4,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,1,0,0]
 => [[3,2,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,1,0,0,0]
 => [[2,2,2,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,1,0,0,0,0]
 => [[3,3,1],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,1,0,0]
 => [[5],[]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,1,0,0]
 => [[4,3],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,1,0,0,0,0]
 => [[4,4],[1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => ([],1)
 => ([],1)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2],[2,1]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2],[3,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [[4,4,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,0,1,1,1,0,0,1,0,0]
 => [[4,3,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [[5,3],[2]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [[4,3,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [[4,4,3],[3,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,0,1,1,0,0,1,1,0,0,0]
 => [[4,4,3],[2,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,1,0,0,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,1,0,0,1,1,0,0]
 => [[4,3,2],[2]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 4
[1,1,1,0,0,1,0,1,1,0,0,0]
 => [[4,4,2],[2]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,1,1,0,0,1,1,0,0,1,0,0]
 => [[4,3,2],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1,1],[1,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1,1],[1,1,1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1,1],[1,1]]
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1,1],[2,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1,1],[2,2]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1,1],[2]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2,1],[1,1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2,1],[2,1,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
 => [[4,2,2,1],[1,1]]
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2,1],[2,2,1]]
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
 => 6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2,1],[2,1]]
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
 => 6
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2,1],[3,1]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 5
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
 => [[5,2,1],[1]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
 => [[4,3,3,1],[2,2]]
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3,1],[3,2]]
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
 => 5
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
 => [[5,3,1],[2]]
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 5
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St000982
(load all 4 compositions to match this statistic)
Mapping
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
St000982: Binary words ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0]
 => 1010 => 0101 => 0000 => 4
[1,1,0,0]
 => 1100 => 0011 => 0110 => 2
[1,0,1,0,1,0]
 => 101010 => 010101 => 000000 => 6
[1,0,1,1,0,0]
 => 101100 => 001101 => 011000 => 3
[1,1,0,0,1,0]
 => 110010 => 010011 => 000110 => 3
[1,1,0,1,0,0]
 => 110100 => 001011 => 011110 => 4
[1,1,1,0,0,0]
 => 111000 => 000111 => 010010 => 2
[1,0,1,0,1,0,1,0]
 => 10101010 => 01010101 => 00000000 => 8
[1,0,1,0,1,1,0,0]
 => 10101100 => 00110101 => 01100000 => 5
[1,0,1,1,0,0,1,0]
 => 10110010 => 01001101 => 00011000 => 3
[1,0,1,1,0,1,0,0]
 => 10110100 => 00101101 => 01111000 => 4
[1,0,1,1,1,0,0,0]
 => 10111000 => 00011101 => 01001000 => 3
[1,1,0,0,1,0,1,0]
 => 11001010 => 01010011 => 00000110 => 5
[1,1,0,0,1,1,0,0]
 => 11001100 => 00110011 => 01100110 => 2
[1,1,0,1,0,0,1,0]
 => 11010010 => 01001011 => 00011110 => 4
[1,1,0,1,0,1,0,0]
 => 11010100 => 00101011 => 01111110 => 6
[1,1,0,1,1,0,0,0]
 => 11011000 => 00011011 => 01001110 => 3
[1,1,1,0,0,0,1,0]
 => 11100010 => 01000111 => 00010010 => 3
[1,1,1,0,0,1,0,0]
 => 11100100 => 00100111 => 01110010 => 3
[1,1,1,0,1,0,0,0]
 => 11101000 => 00010111 => 01000010 => 4
[1,1,1,1,0,0,0,0]
 => 11110000 => 00001111 => 01011010 => 2
[1,0,1,0,1,0,1,0,1,0]
 => 1010101010 => 0101010101 => 0000000000 => 10
[1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => 0011010101 => 0110000000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,0,1,1,0,0,1,0]
 => 1010110010 => 0100110101 => 0001100000 => 5
[1,0,1,0,1,1,0,1,0,0]
 => 1010110100 => 0010110101 => 0111100000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,0,1,1,1,0,0,0]
 => 1010111000 => 0001110101 => 0100100000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,1,0,0,1,0,1,0]
 => 1011001010 => 0101001101 => 0000011000 => 5
[1,0,1,1,0,0,1,1,0,0]
 => 1011001100 => 0011001101 => 0110011000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,1,0,1,0,0,1,0]
 => 1011010010 => 0100101101 => 0001111000 => 4
[1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => 0010101101 => 0111111000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,1,0,1,1,0,0,0]
 => 1011011000 => 0001101101 => 0100111000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,1,1,0,0,0,1,0]
 => 1011100010 => 0100011101 => 0001001000 => 3
[1,0,1,1,1,0,0,1,0,0]
 => 1011100100 => 0010011101 => 0111001000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,1,1,0,1,0,0,0]
 => 1011101000 => 0001011101 => 0100001000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,1,1,1,0,0,0,0]
 => 1011110000 => 0000111101 => 0101101000 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,0,1,0,1,0,1,0]
 => 1100101010 => 0101010011 => 0000000110 => 7
[1,1,0,0,1,0,1,1,0,0]
 => 1100101100 => 0011010011 => 0110000110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,0,1,1,0,0,1,0]
 => 1100110010 => 0100110011 => 0001100110 => 3
[1,1,0,0,1,1,0,1,0,0]
 => 1100110100 => 0010110011 => 0111100110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,0,1,1,1,0,0,0]
 => 1100111000 => 0001110011 => 0100100110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,1,0,0,1,0,1,0]
 => 1101001010 => 0101001011 => 0000011110 => 5
[1,1,0,1,0,0,1,1,0,0]
 => 1101001100 => 0011001011 => 0110011110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,1,0,1,0,0,1,0]
 => 1101010010 => 0100101011 => 0001111110 => 6
[1,1,0,1,0,1,0,1,0,0]
 => 1101010100 => 0010101011 => 0111111110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,1,0,1,1,0,0,0]
 => 1101011000 => 0001101011 => 0100111110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,1,1,0,0,0,1,0]
 => 1101100010 => 0100011011 => 0001001110 => 3
[1,1,0,1,1,0,0,1,0,0]
 => 1101100100 => 0010011011 => 0111001110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,1,1,0,1,0,0,0]
 => 1101101000 => 0001011011 => 0100001110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,0,1,1,1,0,0,0,0]
 => 1101110000 => 0000111011 => 0101101110 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,0,0,0,1,0,1,0]
 => 1110001010 => 0101000111 => 0000010010 => 5
[1,1,1,0,0,0,1,1,0,0]
 => 1110001100 => 0011000111 => 0110010010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,0,0,1,0,0,1,0]
 => 1110010010 => 0100100111 => 0001110010 => 3
[1,1,1,0,0,1,0,1,0,0]
 => 1110010100 => 0010100111 => 0111110010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,0,0,1,1,0,0,0]
 => 1110011000 => 0001100111 => 0100110010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,0,1,0,0,0,1,0]
 => 1110100010 => 0100010111 => 0001000010 => 4
[1,1,1,0,1,0,0,1,0,0]
 => 1110100100 => 0010010111 => 0111000010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,0,1,0,1,0,0,0]
 => 1110101000 => 0001010111 => 0100000010 => 6
[1,1,1,0,1,1,0,0,0,0]
 => 1110110000 => 0000110111 => 0101100010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,1,0,0,0,0,1,0]
 => 1111000010 => 0100001111 => 0001011010 => 3
[1,1,1,1,0,0,0,1,0,0]
 => 1111000100 => 0010001111 => 0111011010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,1,0,0,1,0,0,0]
 => 1111001000 => 0001001111 => 0100011010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,1,0,1,0,0,0,0]
 => 1111010000 => 0000101111 => 0101111010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,1,1,1,1,0,0,0,0,0]
 => 1111100000 => 0000011111 => 0101001010 => ? ∊ {2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,7,8}
[1,0,1,0,1,0,1,0,1,0,1,0]
 => 101010101010 => 010101010101 => 000000000000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,0,1,1,0,0]
 => 101010101100 => 001101010101 => 011000000000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,0,1,0]
 => 101010110010 => 010011010101 => 000110000000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,1,0,0]
 => 101010110100 => 001011010101 => 011110000000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,1,0,0,0]
 => 101010111000 => 000111010101 => 010010000000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,0,0,1,0,1,0]
 => 101011001010 => 010100110101 => 000001100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,0,0,1,1,0,0]
 => 101011001100 => 001100110101 => 011001100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,0,1,0,0,1,0]
 => 101011010010 => 010010110101 => 000111100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,0,1,0,1,0,0]
 => 101011010100 => 001010110101 => 011111100000 => 6
[1,0,1,0,1,1,0,1,1,0,0,0]
 => 101011011000 => 000110110101 => 010011100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,1,0,0,0,1,0]
 => 101011100010 => 010001110101 => 000100100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,1,0,0,1,0,0]
 => 101011100100 => 001001110101 => 011100100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,1,0,1,0,0,0]
 => 101011101000 => 000101110101 => 010000100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,0,1,1,1,1,0,0,0,0]
 => 101011110000 => 000011110101 => 010110100000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,0,1,0,1,0,1,0]
 => 101100101010 => 010101001101 => 000000011000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,0,1,0,1,1,0,0]
 => 101100101100 => 001101001101 => 011000011000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,0,1,1,0,0,1,0]
 => 101100110010 => 010011001101 => 000110011000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,0,1,1,0,1,0,0]
 => 101100110100 => 001011001101 => 011110011000 => 4
[1,0,1,1,0,0,1,1,1,0,0,0]
 => 101100111000 => 000111001101 => 010010011000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,1,0,0,1,0,1,0]
 => 101101001010 => 010100101101 => 000001111000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,1,0,0,1,1,0,0]
 => 101101001100 => 001100101101 => 011001111000 => 4
[1,0,1,1,0,1,0,1,0,0,1,0]
 => 101101010010 => 010010101101 => 000111111000 => 6
[1,0,1,1,0,1,0,1,0,1,0,0]
 => 101101010100 => 001010101101 => 011111111000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,1,0,1,1,0,0,0]
 => 101101011000 => 000110101101 => 010011111000 => 5
[1,0,1,1,0,1,1,0,0,0,1,0]
 => 101101100010 => 010001101101 => 000100111000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,1,1,0,0,1,0,0]
 => 101101100100 => 001001101101 => 011100111000 => 3
[1,0,1,1,0,1,1,0,1,0,0,0]
 => 101101101000 => 000101101101 => 010000111000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,0,1,1,1,0,0,0,0]
 => 101101110000 => 000011101101 => 010110111000 => 3
[1,0,1,1,1,0,0,0,1,0,1,0]
 => 101110001010 => 010100011101 => 000001001000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,1,0,0,0,1,1,0,0]
 => 101110001100 => 001100011101 => 011001001000 => ? ∊ {2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12}
[1,0,1,1,1,0,0,1,0,1,0,0]
 => 101110010100 => 001010011101 => 011111001000 => 5
[1,0,1,1,1,1,0,0,0,1,0,0]
 => 101111000100 => 001000111101 => 011101101000 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => 101111010000 => 000010111101 => 010111101000 => 4
[1,1,0,0,1,0,1,1,0,1,0,0]
 => 110010110100 => 001011010011 => 011110000110 => 4
[1,1,0,0,1,1,0,0,1,1,0,0]
 => 110011001100 => 001100110011 => 011001100110 => 2
[1,1,0,0,1,1,0,1,0,0,1,0]
 => 110011010010 => 010010110011 => 000111100110 => 4
[1,1,0,0,1,1,1,0,0,1,0,0]
 => 110011100100 => 001001110011 => 011100100110 => 3
Description
The length of the longest constant subword.
Matching statistic: St000983
(load all 6 compositions to match this statistic)
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St000983: Binary words ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0]
 => [1]
 => [1,0,1,0]
 => 1010 => 4
[1,1,0,0]
 => []
 => []
 => => ? = 2
[1,0,1,0,1,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => 6
[1,0,1,1,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => 3
[1,1,0,0,1,0]
 => [2]
 => [1,1,0,0,1,0]
 => 110010 => 3
[1,1,0,1,0,0]
 => [1]
 => [1,0,1,0]
 => 1010 => 4
[1,1,1,0,0,0]
 => []
 => []
 => => ? = 2
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 8
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => 5
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => 10110010 => 3
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => 4
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => 3
[1,1,0,0,1,0,1,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => 11001010 => 5
[1,1,0,0,1,1,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 11001100 => 2
[1,1,0,1,0,0,1,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => 11010010 => 4
[1,1,0,1,0,1,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => 6
[1,1,0,1,1,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => 3
[1,1,1,0,0,0,1,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => 3
[1,1,1,0,0,1,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => 110010 => 3
[1,1,1,0,1,0,0,0]
 => [1]
 => [1,0,1,0]
 => 1010 => 4
[1,1,1,1,0,0,0,0]
 => []
 => []
 => => ? = 2
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => 1010101010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => 1010110010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => 1010110100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => 1010111000 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => 1011001010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => 1011001100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => 1011010010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => 1011011000 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => 1011100010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => 1011100100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => 1011101000 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => 1011110000 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => 1100101010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => 1100101100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => 1100110010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => 1100110100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => 1100111000 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => 1101001010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => 1101001100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => 1101010010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 8
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => 5
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => 1101100010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => 10110010 => 3
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => 4
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => 1110001010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,1,0,0,0,1,1,0,0]
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => 1110001100 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,1,0,0,1,0,0,1,0]
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => 1110010010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => 11001010 => 5
[1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 11001100 => 2
[1,1,1,0,1,0,0,0,1,0]
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => 1110100010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,1,0,1,0,0,1,0,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => 11010010 => 4
[1,1,1,0,1,0,1,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => 6
[1,1,1,0,1,1,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1111000010 => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,1,1,1,0,0,0,1,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => 3
[1,1,1,1,0,0,1,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => 110010 => 3
[1,1,1,1,0,1,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => 1010 => 4
[1,1,1,1,1,0,0,0,0,0]
 => []
 => []
 => => ? ∊ {2,2,2,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,7,7,10}
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [5,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => 101010101010 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [4,4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => 101010101100 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => 101010110010 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [4,3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => 101010110100 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [3,3,3,2,1]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => 101010111000 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [5,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => 101011001010 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => 101011001100 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [5,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => 101011010010 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [4,3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => 101011010100 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [3,3,2,2,1]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => 101011011000 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [5,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => 101011100010 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [4,2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => 101011100100 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [3,2,2,2,1]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => 101011101000 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => 101011110000 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [5,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => 101100101010 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [4,4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => 101100101100 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [5,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 101100110010 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [4,3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => 101100110100 => ? ∊ {2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,9,9,10,12}
[1,1,1,0,1,0,1,0,1,0,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 8
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => 5
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => 10110010 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => 3
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => 11001010 => 5
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => 11001100 => 2
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => 11010010 => 4
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [2,1]
 => [1,0,1,0,1,0]
 => 101010 => 6
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,1]
 => [1,0,1,1,0,0]
 => 101100 => 3
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => 11100010 => 3
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [2]
 => [1,1,0,0,1,0]
 => 110010 => 3
[1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => [1,0,1,0]
 => 1010 => 4
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => 10110010 => 3
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => 10111000 => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => 11001010 => 5
Description
The length of the longest alternating subword. This is the length of the longest consecutive subword of the form $010...$ or of the form $101...$.
Matching statistic: St001198
(load all 3 compositions to match this statistic)
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 25%
Values
[1,0,1,0]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => ? ∊ {2,4}
[1,1,0,0]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => ? ∊ {2,4}
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,0,1,1,0,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 3
[1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 3
Description
The 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 $eA$.
Matching statistic: St001206
(load all 3 compositions to match this statistic)
Mapping
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 25%
Values
[1,0,1,0]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => ? ∊ {2,4}
[1,1,0,0]
 => [1,0,1,0]
 => [1,0,1,0]
 => [1,1,0,0]
 => ? ∊ {2,4}
[1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,0,1,1,0,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,1,0,0,1,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,1,1,0,0,0]
 => [1,0,1,0,1,0]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => ? ∊ {2,3,3,4,6}
[1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => ? ∊ {2,2,3,3,3,3,4,4,4,5,5,6,8}
[1,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => 3
[1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,0,1,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,0,1,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => ? ∊ {2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,7,7,8,10}
[1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => 2
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
[1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,0,0,1,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
[1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,0,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,0,1,0,1,1,0,0,0,0]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,0,1,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,0,1,0,0,0]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,1,1,0,1,0,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => 4
[1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,1,0,0,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,0,1,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,0,1,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,0,1,0,0,0]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,0,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,1,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,1,1,0,1,0,1,0,0,0,0]
 => 3
[1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => 3
[1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => 3
Description
The 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 $eA$.
Matching statistic: St000392
Mapping
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00200: Binary words —twist⟶ Binary words
St000392: Binary words ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 67%
Values
[1,0,1,0]
 => 1010 => 1111 => 0111 => 3 = 4 - 1
[1,1,0,0]
 => 1100 => 1001 => 0001 => 1 = 2 - 1
[1,0,1,0,1,0]
 => 101010 => 111111 => 011111 => 5 = 6 - 1
[1,0,1,1,0,0]
 => 101100 => 111001 => 011001 => 2 = 3 - 1
[1,1,0,0,1,0]
 => 110010 => 100111 => 000111 => 3 = 4 - 1
[1,1,0,1,0,0]
 => 110100 => 100001 => 000001 => 1 = 2 - 1
[1,1,1,0,0,0]
 => 111000 => 101101 => 001101 => 2 = 3 - 1
[1,0,1,0,1,0,1,0]
 => 10101010 => 11111111 => 01111111 => 7 = 8 - 1
[1,0,1,0,1,1,0,0]
 => 10101100 => 11111001 => 01111001 => 4 = 5 - 1
[1,0,1,1,0,0,1,0]
 => 10110010 => 11100111 => 01100111 => 3 = 4 - 1
[1,0,1,1,0,1,0,0]
 => 10110100 => 11100001 => 01100001 => 2 = 3 - 1
[1,0,1,1,1,0,0,0]
 => 10111000 => 11101101 => 01101101 => 2 = 3 - 1
[1,1,0,0,1,0,1,0]
 => 11001010 => 10011111 => 00011111 => 5 = 6 - 1
[1,1,0,0,1,1,0,0]
 => 11001100 => 10011001 => 00011001 => 2 = 3 - 1
[1,1,0,1,0,0,1,0]
 => 11010010 => 10000111 => 00000111 => 3 = 4 - 1
[1,1,0,1,0,1,0,0]
 => 11010100 => 10000001 => 00000001 => 1 = 2 - 1
[1,1,0,1,1,0,0,0]
 => 11011000 => 10001101 => 00001101 => 2 = 3 - 1
[1,1,1,0,0,0,1,0]
 => 11100010 => 10110111 => 00110111 => 3 = 4 - 1
[1,1,1,0,0,1,0,0]
 => 11100100 => 10110001 => 00110001 => 2 = 3 - 1
[1,1,1,0,1,0,0,0]
 => 11101000 => 10111101 => 00111101 => 4 = 5 - 1
[1,1,1,1,0,0,0,0]
 => 11110000 => 10100101 => 00100101 => 1 = 2 - 1
[1,0,1,0,1,0,1,0,1,0]
 => 1010101010 => 1111111111 => 0111111111 => 9 = 10 - 1
[1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => 1111111001 => 0111111001 => 6 = 7 - 1
[1,0,1,0,1,1,0,0,1,0]
 => 1010110010 => 1111100111 => 0111100111 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,0,1,0,1,1,0,1,0,0]
 => 1010110100 => 1111100001 => 0111100001 => 4 = 5 - 1
[1,0,1,0,1,1,1,0,0,0]
 => 1010111000 => 1111101101 => 0111101101 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,0,1,1,0,0,1,0,1,0]
 => 1011001010 => 1110011111 => 0110011111 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,0,1,1,0,0,1,1,0,0]
 => 1011001100 => 1110011001 => 0110011001 => 2 = 3 - 1
[1,0,1,1,0,1,0,0,1,0]
 => 1011010010 => 1110000111 => 0110000111 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => 1110000001 => 0110000001 => 2 = 3 - 1
[1,0,1,1,0,1,1,0,0,0]
 => 1011011000 => 1110001101 => 0110001101 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,0,1,1,1,0,0,0,1,0]
 => 1011100010 => 1110110111 => 0110110111 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,0,1,1,1,0,0,1,0,0]
 => 1011100100 => 1110110001 => 0110110001 => 2 = 3 - 1
[1,0,1,1,1,0,1,0,0,0]
 => 1011101000 => 1110111101 => 0110111101 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,0,1,1,1,1,0,0,0,0]
 => 1011110000 => 1110100101 => 0110100101 => 2 = 3 - 1
[1,1,0,0,1,0,1,0,1,0]
 => 1100101010 => 1001111111 => 0001111111 => 7 = 8 - 1
[1,1,0,0,1,0,1,1,0,0]
 => 1100101100 => 1001111001 => 0001111001 => 4 = 5 - 1
[1,1,0,0,1,1,0,0,1,0]
 => 1100110010 => 1001100111 => 0001100111 => 3 = 4 - 1
[1,1,0,0,1,1,0,1,0,0]
 => 1100110100 => 1001100001 => 0001100001 => 2 = 3 - 1
[1,1,0,0,1,1,1,0,0,0]
 => 1100111000 => 1001101101 => 0001101101 => 2 = 3 - 1
[1,1,0,1,0,0,1,0,1,0]
 => 1101001010 => 1000011111 => 0000011111 => 5 = 6 - 1
[1,1,0,1,0,0,1,1,0,0]
 => 1101001100 => 1000011001 => 0000011001 => 2 = 3 - 1
[1,1,0,1,0,1,0,0,1,0]
 => 1101010010 => 1000000111 => 0000000111 => 3 = 4 - 1
[1,1,0,1,0,1,0,1,0,0]
 => 1101010100 => 1000000001 => 0000000001 => 1 = 2 - 1
[1,1,0,1,0,1,1,0,0,0]
 => 1101011000 => 1000001101 => 0000001101 => 2 = 3 - 1
[1,1,0,1,1,0,0,0,1,0]
 => 1101100010 => 1000110111 => 0000110111 => 3 = 4 - 1
[1,1,0,1,1,0,0,1,0,0]
 => 1101100100 => 1000110001 => 0000110001 => 2 = 3 - 1
[1,1,0,1,1,0,1,0,0,0]
 => 1101101000 => 1000111101 => 0000111101 => 4 = 5 - 1
[1,1,0,1,1,1,0,0,0,0]
 => 1101110000 => 1000100101 => 0000100101 => 1 = 2 - 1
[1,1,1,0,0,0,1,0,1,0]
 => 1110001010 => 1011011111 => 0011011111 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,1,1,0,0,0,1,1,0,0]
 => 1110001100 => 1011011001 => 0011011001 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,1,1,0,0,1,0,0,1,0]
 => 1110010010 => 1011000111 => 0011000111 => 3 = 4 - 1
[1,1,1,0,0,1,0,1,0,0]
 => 1110010100 => 1011000001 => 0011000001 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,1,1,0,0,1,1,0,0,0]
 => 1110011000 => 1011001101 => 0011001101 => 2 = 3 - 1
[1,1,1,0,1,0,0,0,1,0]
 => 1110100010 => 1011110111 => 0011110111 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,1,1,0,1,0,0,1,0,0]
 => 1110100100 => 1011110001 => 0011110001 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,1,1,0,1,0,1,0,0,0]
 => 1110101000 => 1011111101 => 0011111101 => 6 = 7 - 1
[1,1,1,0,1,1,0,0,0,0]
 => 1110110000 => 1011100101 => 0011100101 => ? ∊ {3,3,3,4,4,4,5,5,5,5,5,6,6} - 1
[1,1,1,1,0,0,0,0,1,0]
 => 1111000010 => 1010010111 => 0010010111 => 3 = 4 - 1
[1,1,1,1,0,0,0,1,0,0]
 => 1111000100 => 1010010001 => 0010010001 => 1 = 2 - 1
[1,1,1,1,0,0,1,0,0,0]
 => 1111001000 => 1010011101 => 0010011101 => 3 = 4 - 1
[1,1,1,1,0,1,0,0,0,0]
 => 1111010000 => 1010000101 => 0010000101 => 1 = 2 - 1
[1,1,1,1,1,0,0,0,0,0]
 => 1111100000 => 1010110101 => 0010110101 => 2 = 3 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => 101010101010 => 111111111111 => 011111111111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
 => 101010101100 => 111111111001 => 011111111001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => 101010110010 => 111111100111 => 011111100111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => 101010110100 => 111111100001 => 011111100001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => 101010111000 => 111111101101 => 011111101101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => 101011001010 => 111110011111 => 011110011111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => 101011001100 => 111110011001 => 011110011001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => 101011010010 => 111110000111 => 011110000111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => 101011010100 => 111110000001 => 011110000001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => 101011011000 => 111110001101 => 011110001101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => 101011100010 => 111110110111 => 011110110111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => 101011100100 => 111110110001 => 011110110001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,1,0,1,0,0,0]
 => 101011101000 => 111110111101 => 011110111101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => 101011110000 => 111110100101 => 011110100101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => 101100101010 => 111001111111 => 011001111111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,0,1,0,1,1,0,0]
 => 101100101100 => 111001111001 => 011001111001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,0,1,1,0,0,1,0]
 => 101100110010 => 111001100111 => 011001100111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => 101100110100 => 111001100001 => 011001100001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => 101100111000 => 111001101101 => 011001101101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => 101101001010 => 111000011111 => 011000011111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,0,0,1,1,0,0]
 => 101101001100 => 111000011001 => 011000011001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,0,1,0,0,1,0]
 => 101101010010 => 111000000111 => 011000000111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,0,1,0,1,0,0]
 => 101101010100 => 111000000001 => 011000000001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,0,1,1,0,0,0]
 => 101101011000 => 111000001101 => 011000001101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => 101101100010 => 111000110111 => 011000110111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,1,0,0,1,0,0]
 => 101101100100 => 111000110001 => 011000110001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,1,0,1,0,0,0]
 => 101101101000 => 111000111101 => 011000111101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,0,1,1,1,0,0,0,0]
 => 101101110000 => 111000100101 => 011000100101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => 101110001010 => 111011011111 => 011011011111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,0,0,1,1,0,0]
 => 101110001100 => 111011011001 => 011011011001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,0,1,0,0,1,0]
 => 101110010010 => 111011000111 => 011011000111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,0,1,0,1,0,0]
 => 101110010100 => 111011000001 => 011011000001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,0,1,1,0,0,0]
 => 101110011000 => 111011001101 => 011011001101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,1,0,0,0,1,0]
 => 101110100010 => 111011110111 => 011011110111 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,1,0,0,1,0,0]
 => 101110100100 => 111011110001 => 011011110001 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,1,0,1,0,0,0]
 => 101110101000 => 111011111101 => 011011111101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
[1,0,1,1,1,0,1,1,0,0,0,0]
 => 101110110000 => 111011100101 => 011011100101 => ? ∊ {2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,9,9,10,12} - 1
Description
The length of the longest run of ones in a binary word.
The following 8 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001645The pebbling number of a connected graph. St001879The 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. St001372The length of a longest cyclic run of ones of a binary word. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St001060The distinguishing index of a graph. St000454The largest eigenvalue of a graph if it is integral. St000381The largest part of an integer composition. St000422The energy of a graph, if it is integral.