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Your data matches 41 different statistics following compositions of up to 3 maps.
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Matching statistic: St001141
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001141: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00312: Integer partitions —Glaisher-Franklin⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001141: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0,1,0]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 0
[1,0,1,1,0,0]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 0
[1,1,0,0,1,0]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 0
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> 0
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 0
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 0
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> 0
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 0
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 0
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> 0
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 0
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 0
[1,1,1,0,0,0,1,0]
=> [3]
=> [3]
=> [1,0,1,0,1,0]
=> 0
[1,1,1,0,0,1,0,0]
=> [2]
=> [1,1]
=> [1,1,0,0]
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [3,2,2,1,1,1]
=> [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=> 0
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [3,1,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> 0
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [3,2,2,2]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> 0
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [6,2]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> 1
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [2,2,2,1,1]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [3,2,1,1]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [2,1,1,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [2,2,2,1]
=> [1,1,1,1,0,0,0,1,0,0]
=> 0
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [3,2,1]
=> [1,0,1,1,1,0,0,1,0,0]
=> 0
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [2,1,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [4]
=> [1,0,1,0,1,0,1,0]
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [3,2,2,1,1]
=> [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> 0
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [6,1,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [2,2,1,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> 0
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [3,1,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [3,2,2,1]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> 0
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [6,1]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [2,2,1,1,1]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> 0
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [3,1,1,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,1,1,1,1]
=> [1,1,0,1,0,1,0,1,0,0]
=> 0
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [2,2,2]
=> [1,1,1,1,0,0,0,0]
=> 0
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [3,2]
=> [1,0,1,1,1,0,0,0]
=> 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [2,1]
=> [1,0,1,1,0,0]
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [3,2,2]
=> [1,0,1,1,1,1,0,0,0,0]
=> 0
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [6]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [2,2,1,1]
=> [1,1,1,0,0,1,0,1,0,0]
=> 0
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [3,1,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 0
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [1,1,1,1]
=> [1,1,0,1,0,1,0,0]
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [2,2,1]
=> [1,1,1,0,0,1,0,0]
=> 0
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [3,1]
=> [1,0,1,0,1,1,0,0]
=> 0
[1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> [1,1,1]
=> [1,1,0,1,0,0]
=> 0
[1,1,1,0,1,1,0,0,0,0]
=> [1,1]
=> [2]
=> [1,0,1,0]
=> 0
Description
The number of occurrences of hills of size 3 in a Dyck path.
A hill of size three is a subpath beginning at height zero, consisting of three up steps followed by three down steps.
Matching statistic: St000264
(load all 17 compositions to match this statistic)
(load all 17 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 50%
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> 3 = 0 + 3
[1,0,1,1,0,0]
=> [2,3,1] => [3,1,2] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,1,0,0,1,0]
=> [3,1,2] => [2,3,1] => ([(0,2),(1,2)],3)
=> ? = 0 + 3
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ? = 1 + 3
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 0 + 3
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
=> 3 = 0 + 3
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,1,2,4] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 0 + 3
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
=> ? = 0 + 3
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [5,2,1,3,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 1 + 3
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [4,1,5,3,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [5,1,4,3,2] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [5,1,4,2,3] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [4,1,3,5,2] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,1,3,4,2] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [5,1,3,2,4] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [2,5,3,1,4] => ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 0 + 3
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [2,5,1,4,3] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 0 + 3
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,2,1,3,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 0 + 3
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 1 + 3
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [4,1,3,2,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 0 + 3
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [2,4,3,1,5] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 0 + 3
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => [3,4,2,1,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5)
=> 3 = 0 + 3
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => [3,1,2,4,5] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 1 + 3
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 0 + 3
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => [2,3,1,4,5] => ([(2,4),(3,4)],5)
=> ? = 0 + 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,6,4,2,3,1] => [3,1,6,4,2,5] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 0 + 3
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [4,5,6,2,3,1] => [3,1,6,2,4,5] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [5,4,3,2,6,1] => [6,1,5,4,3,2] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [4,3,5,2,6,1] => [6,1,5,2,4,3] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [3,4,5,2,6,1] => [6,1,5,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [5,6,2,3,4,1] => [4,1,3,6,2,5] => ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [6,4,2,3,5,1] => [5,1,3,6,4,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [5,4,2,3,6,1] => [6,1,3,5,4,2] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [4,5,2,3,6,1] => [6,1,3,5,2,4] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [5,3,2,4,6,1] => [6,1,4,5,3,2] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [4,3,2,5,6,1] => [6,1,4,3,2,5] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [3,4,2,5,6,1] => [6,1,4,2,3,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [6,2,3,4,5,1] => [5,1,3,4,6,2] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [5,2,3,4,6,1] => [6,1,3,4,5,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [4,2,3,5,6,1] => [6,1,3,4,2,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [3,2,4,5,6,1] => [6,1,3,2,4,5] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [6,1,2,3,4,5] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 0 + 3
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,6,4,2,1,3] => [3,6,4,2,1,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,1,3] => [3,5,2,1,6,4] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [4,5,6,2,1,3] => [3,6,2,1,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> 3 = 0 + 3
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [5,6,2,3,1,4] => [3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 0 + 3
[1,1,0,1,1,0,0,1,1,0,0,0]
=> [4,5,2,3,1,6] => [3,1,5,2,4,6] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ? = 1 + 3
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,1,6] => [5,1,2,3,4,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 0 + 3
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [6,4,5,1,2,3] => [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [4,5,6,1,2,3] => [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,1,1,0,0,1,1,0,0,1,0,0]
=> [5,3,4,1,2,6] => [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ? = 0 + 3
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,4,5,1,2,6] => [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,1,1,0,1,1,0,0,0,0,1,0]
=> [6,2,3,1,4,5] => [3,1,4,5,6,2] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 1 + 3
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [5,2,3,1,4,6] => [3,1,4,5,2,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [4,2,3,1,5,6] => [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6)
=> ? = 1 + 3
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,3,4,1,5,6] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6)
=> ? = 0 + 3
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [5,6,1,2,3,4] => [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [4,5,1,2,3,6] => [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [3,4,1,2,5,6] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6)
=> ? = 0 + 3
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,3,1,4,5,6] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6)
=> ? = 0 + 3
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [6,1,2,3,4,5] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 0 + 3
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,1,2,3,4,6] => [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 1 + 3
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [4,1,2,3,5,6] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6)
=> ? = 0 + 3
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [3,1,2,4,5,6] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6)
=> ? = 0 + 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 1 + 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [6,4,5,2,3,1,7] => [3,1,5,2,6,4,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6)],7)
=> ? = 0 + 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [4,5,6,2,3,1,7] => [3,1,6,2,4,5,7] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 0 + 3
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 0 + 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [5,6,2,3,1,4,7] => [3,1,4,6,2,5,7] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ? = 0 + 3
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [4,5,2,3,1,6,7] => [3,1,5,2,4,6,7] => ([(2,6),(3,5),(4,5),(4,6)],7)
=> ? = 1 + 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 0 + 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: St001603
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [2,3,1] => [2,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0]
=> [2,1,3] => [2,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0]
=> [1,3,2] => [2,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => [2,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => [2,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,5,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,1,5,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [3,1,4,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [3,5,1,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [4,1,5,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,1,5,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,0,1,0]
=> [4,5,1,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,5,1,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,1,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [2,1,3,6,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [2,1,3,6,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [2,1,6,3,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,1,6,3,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [2,1,6,7,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [2,6,1,3,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [2,6,1,3,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [2,6,1,7,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,6,7,1,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [3,1,5,6,2,4,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [3,1,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [3,5,6,7,1,2,4] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [3,5,7,1,2,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [3,1,6,2,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [3,1,6,2,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [3,1,6,7,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [3,6,1,7,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [3,6,7,1,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [4,1,5,6,2,3,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> [4,1,5,2,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,7,1,2,3] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [4,5,7,1,2,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [4,1,2,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [4,1,2,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [4,1,6,2,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=> [4,1,6,2,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=> [4,1,6,7,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=> [4,6,1,2,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [4,6,1,2,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [4,6,1,7,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [4,6,7,1,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> [1,5,6,2,3,7,4] => [4,3]
=> [3]
=> 1 = 0 + 1
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001604
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [2,3,1] => [2,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0]
=> [2,1,3] => [2,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0]
=> [1,3,2] => [2,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => [2,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => [2,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,5,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,1,5,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [3,1,4,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [3,5,1,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [4,1,5,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,1,5,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,0,1,0]
=> [4,5,1,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,5,1,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,1,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [2,1,3,6,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [2,1,3,6,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [2,1,6,3,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,1,6,3,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [2,1,6,7,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [2,6,1,3,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [2,6,1,3,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [2,6,1,7,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,6,7,1,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [3,1,5,6,2,4,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [3,1,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [3,5,6,7,1,2,4] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [3,5,7,1,2,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [3,1,6,2,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [3,1,6,2,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [3,1,6,7,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [3,6,1,7,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [3,6,7,1,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [4,1,5,6,2,3,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> [4,1,5,2,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,7,1,2,3] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [4,5,7,1,2,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [4,1,2,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [4,1,2,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [4,1,6,2,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=> [4,1,6,2,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=> [4,1,6,7,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=> [4,6,1,2,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [4,6,1,2,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [4,6,1,7,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [4,6,7,1,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> [1,5,6,2,3,7,4] => [4,3]
=> [3]
=> 1 = 0 + 1
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001605
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [2,3,1] => [2,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0]
=> [2,1,3] => [2,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0]
=> [1,3,2] => [2,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0]
=> [2,3,4,1] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [2,3,1,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [2,1,4,3] => [2,2]
=> [2]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0]
=> [2,4,1,3] => [2,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [2,1,3,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,3,4,2] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0]
=> [1,3,2,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0]
=> [3,1,4,2] => [2,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0]
=> [3,4,1,2] => [2,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0]
=> [3,1,2,4] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0]
=> [1,2,4,3] => [3,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0]
=> [1,4,2,3] => [3,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,3,5,1,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,3,1,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,4,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,5] => [3,2]
=> [2]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [2,4,1,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [2,4,5,1,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,4,1,3,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [2,1,3,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [2,1,5,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,5,1,3,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,3,4,2,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,3,5,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,3,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,4,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,1,4,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [3,4,1,5,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,4,5,1,2] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,1,2,5] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [3,1,2,5,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,5,2,4] => [3,2]
=> [2]
=> ? = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,5,1,2,4] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [3,1,2,4,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,2,4,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,4,2,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,5,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,2,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,5,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,0,0,1,0,0]
=> [4,1,5,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,0,1,0,0,0]
=> [4,5,1,2,3] => [3,2]
=> [2]
=> ? = 0 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [4,1,2,3,5] => [4,1]
=> [1]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,4,6,1,3,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,5,3,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,1,5,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [2,5,1,6,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [2,5,6,1,3,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [3,1,4,2,6,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [3,4,6,1,2,5] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [3,1,5,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,0,0]
=> [3,1,5,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,0,1,0]
=> [3,5,1,2,6,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [3,5,1,6,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [3,5,6,1,2,4] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [4,1,5,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [4,1,5,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,0,1,0]
=> [4,5,1,2,6,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [4,5,1,6,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,1,2,3] => [3,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [2,1,3,6,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [2,1,3,6,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=> [2,1,6,3,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [2,1,6,3,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [2,1,6,7,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=> [2,6,1,3,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=> [2,6,1,3,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [2,6,1,7,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [2,6,7,1,3,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [3,1,5,6,2,4,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [3,1,5,2,7,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [3,5,6,7,1,2,4] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [3,5,7,1,2,4,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [3,1,6,2,4,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [3,1,6,2,7,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=> [3,1,6,7,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [3,6,1,7,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [3,6,7,1,2,4,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [4,1,5,6,2,3,7] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> [4,1,5,2,7,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [4,5,6,7,1,2,3] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [4,5,7,1,2,3,6] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [4,1,2,6,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [4,1,2,6,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [4,1,6,2,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=> [4,1,6,2,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=> [4,1,6,7,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=> [4,6,1,2,3,7,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [4,6,1,2,7,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [4,6,1,7,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [4,6,7,1,2,3,5] => [4,3]
=> [3]
=> 1 = 0 + 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> [1,5,6,2,3,7,4] => [4,3]
=> [3]
=> 1 = 0 + 1
Description
The number of colourings of a cycle such that the multiplicities of colours are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the cyclic group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Matching statistic: St001498
(load all 15 compositions to match this statistic)
(load all 15 compositions to match this statistic)
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [1,1,0,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 0
[1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 0
[1,1,0,0,1,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 0
[1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> 0
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 0
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 0
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 0
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 0
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> 0
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> 0
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 0
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0
[1,1,1,0,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[1,1,1,0,1,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 0
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> 0
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 0
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> 0
Description
The normalised height of a Nakayama algebra with magnitude 1.
We use the bijection (see code) suggested by Christian Stump, to have a bijection between such Nakayama algebras with magnitude 1 and Dyck paths. The normalised height is the height of the (periodic) Dyck path given by the top of the Auslander-Reiten quiver. Thus when having a CNakayama algebra it is the Loewy length minus the number of simple modules and for the LNakayama algebras it is the usual height.
Matching statistic: St001199
(load all 11 compositions to match this statistic)
(load all 11 compositions to match this statistic)
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00118: Dyck paths —swap returns and last descent⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [1,1,0,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,1,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> 1 = 0 + 1
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001876
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001876: Lattices ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ([],3)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> ([(0,1),(0,2)],3)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> ([(0,2),(1,2)],3)
=> ([],1)
=> ? = 0
[1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ([],4)
=> ([],1)
=> ? = 0
[1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> ([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ? = 0
[1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> ([(1,2),(1,3)],4)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0]
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0
[1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0
[1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ? = 0
[1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> ([(1,3),(2,3)],4)
=> ([],1)
=> ? = 0
[1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ([],5)
=> ([],1)
=> ? = 0
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> ([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> ([(2,3),(2,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ? = 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> ([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> ([(2,4),(3,4)],5)
=> ([],1)
=> ? = 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],1)
=> ? = 0
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([],1)
=> ? = 0
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,6),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,5)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,3),(6,2),(6,3)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=> ([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7)
=> ([(0,2),(2,1)],3)
=> 0
Description
The number of 2-regular simple modules in the incidence algebra of the lattice.
Matching statistic: St001877
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001877: Lattices ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ([],3)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> ([(0,1),(0,2)],3)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> ([(0,2),(1,2)],3)
=> ([],1)
=> ? = 0
[1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ([],4)
=> ([],1)
=> ? = 0
[1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> ([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ? = 0
[1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> ([(1,2),(1,3)],4)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0]
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0
[1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0
[1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ? = 0
[1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> ([(1,3),(2,3)],4)
=> ([],1)
=> ? = 0
[1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ([],5)
=> ([],1)
=> ? = 0
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ? = 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> ([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ? = 0
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> ([(2,3),(2,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([],1)
=> ? = 0
[1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ? = 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> ([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(3,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 0
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> ([(2,4),(3,4)],5)
=> ([],1)
=> ? = 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ? = 0
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],1)
=> ? = 0
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],1)
=> ? = 0
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([],1)
=> ? = 0
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ? = 0
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,6),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,5)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,3),(6,2),(6,3)],7)
=> ([(0,2),(2,1)],3)
=> 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=> ([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7)
=> ([(0,2),(2,1)],3)
=> 0
Description
Number of indecomposable injective modules with projective dimension 2.
Matching statistic: St001878
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001878: Lattices ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 50%
Values
[1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ([],3)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> ([(0,1),(0,2)],3)
=> ([],1)
=> ? = 0 + 1
[1,1,0,0,1,0]
=> [1,0,1,1,0,0]
=> ([(0,2),(1,2)],3)
=> ([],1)
=> ? = 0 + 1
[1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ([],4)
=> ([],1)
=> ? = 0 + 1
[1,0,1,0,1,1,0,0]
=> [1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3)],4)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ? = 1 + 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> ([(0,3),(3,1),(3,2)],4)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,0,0]
=> ([(1,2),(1,3)],4)
=> ([],1)
=> ? = 0 + 1
[1,1,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,0]
=> ([(0,3),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0 + 1
[1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([],1)
=> ? = 0 + 1
[1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0]
=> ([(0,3),(1,3),(3,2)],4)
=> ([],1)
=> ? = 0 + 1
[1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,0]
=> ([(1,3),(2,3)],4)
=> ([],1)
=> ? = 0 + 1
[1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ([],5)
=> ([],1)
=> ? = 0 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([],1)
=> ? = 0 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> ([(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 1 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(4,2),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> ([(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> ([(2,3),(2,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,1)],2)
=> ? = 1 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(3,4)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> ([(1,4),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(3,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> ([],1)
=> ? = 0 + 1
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ([(0,4),(1,4),(2,3),(2,4)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> ([(2,4),(3,4)],5)
=> ([],1)
=> ? = 1 + 1
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(4,1)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ([(0,4),(1,2),(1,3),(1,4)],5)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ([],1)
=> ? = 0 + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ? = 0 + 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 0 + 1
[1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=> ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,6),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 0 + 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> ([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,5)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)
=> ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=> ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,3),(6,2),(6,3)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=> ([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7)
=> ([(0,2),(2,1)],3)
=> 1 = 0 + 1
Description
The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.
The following 31 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001330The hat guessing number of a graph. St001625The Möbius invariant of a lattice. St001621The number of atoms of a lattice. St001198The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$. St001206The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$. St000782The indicator function of whether a given perfect matching is an L & P matching. St001845The number of join irreducibles minus the rank of a lattice. St000181The number of connected components of the Hasse diagram for the poset. St001490The number of connected components of a skew partition. St001890The maximum magnitude of the Möbius function of a poset. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001722The number of minimal chains with small intervals between a binary word and the top element. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St000214The number of adjacencies of a permutation. St000215The number of adjacencies of a permutation, zero appended. St000768The number of peaks in an integer composition. St001866The nesting alignments of a signed permutation. St001095The number of non-isomorphic posets with precisely one further covering relation. St001301The first Betti number of the order complex associated with the poset. St001396Number of triples of incomparable elements in a finite poset. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001533The largest coefficient of the Poincare polynomial of the poset cone. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St000454The largest eigenvalue of a graph if it is integral. St000007The number of saliances of the permutation. St000405The number of occurrences of the pattern 1324 in a permutation. St001964The interval resolution global dimension of a poset. St000741The Colin de Verdière graph invariant. St000842The breadth of a permutation.
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