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Your data matches 9 different statistics following compositions of up to 3 maps.
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Matching statistic: St001630
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,1,0,0,0]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,0]
=> [2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,0,1,0,1,0]
=> [3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,5,3] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,5,3,4] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,1,0,0,1,0,1,0,1,0]
=> [3,1,4,2,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [3,1,4,5,2] => ([(0,4),(1,2),(1,4),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [3,4,1,5,2] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 2
[1,1,0,1,0,1,0,0,1,0]
=> [3,1,2,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,1,5,2,3] => ([(0,4),(1,2),(1,4),(2,3)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,1,2,5,3] => ([(0,4),(1,2),(2,3),(2,4)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,5,2,3,4] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,2),(2,1)],3)
=> 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,1,4,3,6,5] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,6,5] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,6,3,5] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,6,3,5] => ([(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
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,4,6,1,3,5] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,1,4,5,3,6] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ([(0,2),(2,1)],3)
=> 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,4,1,5,3,6] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,4,5,1,3,6] => ([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,1,4,5,6,3] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,4,1,5,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,4,5,1,6,3] => ([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(3,2),(4,3)],6)
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [2,1,5,3,6,4] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ([(0,3),(2,1),(3,2)],4)
=> 2
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Matching statistic: St000264
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 50%
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 50%
Values
[1,1,1,0,0,0]
=> [1,2,3] => ([],3)
=> ? = 1 + 2
[1,0,1,0,1,1,0,0]
=> [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ? = 1 + 2
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 2
[1,1,0,0,1,0,1,0]
=> [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ? = 1 + 2
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4 = 2 + 2
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
=> ? = 1 + 2
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => ([],4)
=> ? = 2 + 2
[1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 1 + 2
[1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2 + 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 2 + 2
[1,0,1,1,0,0,1,0,1,0]
=> [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0]
=> [2,5,1,3,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 2
[1,0,1,1,0,1,0,1,0,0]
=> [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,3,5,1,4] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,0,0,1,0,1,0,1,0]
=> [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5)
=> ? = 1 + 2
[1,1,0,0,1,0,1,1,0,0]
=> [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 2 + 2
[1,1,0,0,1,1,0,0,1,0]
=> [3,1,4,5,2] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 2
[1,1,0,0,1,1,0,1,0,0]
=> [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 2 + 2
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 2 + 2
[1,1,0,1,0,0,1,0,1,0]
=> [3,1,5,2,4] => ([(0,4),(1,3),(2,3),(2,4)],5)
=> ? = 2 + 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 2 + 2
[1,1,0,1,0,1,0,0,1,0]
=> [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,1,0,1,0,1,1,0,0,0]
=> [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5)
=> ? = 1 + 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,1,1,0,0,0,1,0,1,0]
=> [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 4 = 2 + 2
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 2 + 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,1,2,5,3] => ([(0,4),(1,4),(2,3),(3,4)],5)
=> ? = 2 + 2
[1,1,1,0,0,1,0,1,0,0]
=> [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5)
=> ? = 1 + 2
[1,1,1,0,0,1,1,0,0,0]
=> [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 4 = 2 + 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,1,1,1,0,0,0,1,0,0]
=> [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => ([],5)
=> ? = 1 + 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
=> ? = 1 + 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ? = 1 + 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6)
=> ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [2,4,1,5,3,6] => ([(1,5),(2,4),(3,4),(3,5)],6)
=> ? = 2 + 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,1,4,5,6,3] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [2,4,1,5,6,3] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 1 + 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [2,5,1,3,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,1,4,6] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 2 + 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [2,3,1,5,6,4] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ? = 2 + 2
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [2,3,5,1,6,4] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [2,1,6,3,4,5] => ([(0,1),(2,5),(3,5),(4,5)],6)
=> ? = 2 + 2
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [2,6,1,3,4,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6)
=> ? = 1 + 2
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [2,3,1,6,4,5] => ([(0,5),(1,5),(2,4),(3,4)],6)
=> ? = 2 + 2
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [2,3,6,1,4,5] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> ? = 1 + 2
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,0,1,1,0,0,0,1,1,0,0]
=> [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [4,1,5,2,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,1,0,0,1,1,0,0]
=> [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,0,1,0,0,0,1,0,1,0]
=> [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,0,1,0,0,0,1,1,0,0]
=> [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,0,0,1,0,1,0]
=> [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,0,1,0,0,1,0]
=> [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 2 + 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [2,4,6,1,3,5,7] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [2,4,6,1,3,7,5] => ([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)
=> 4 = 2 + 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [2,1,4,6,7,3,5] => ([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 2 + 2
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St001199
(load all 3 compositions to match this statistic)
(load all 3 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: 30% ●values known / values provided: 30%●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: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 50%
Values
[1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 1 - 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]
=> ? = 1 - 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]
=> ? = 1 - 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]
=> ? = 1 - 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 = 2 - 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]
=> ? = 1 - 1
[1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 2 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 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]
=> ? = 2 - 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 = 2 - 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]
=> ? = 1 - 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]
=> ? = 2 - 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]
=> ? = 1 - 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]
=> ? = 2 - 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]
=> ? = 1 - 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]
=> ? = 2 - 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]
=> ? = 1 - 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 = 2 - 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]
=> ? = 2 - 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 = 2 - 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 = 2 - 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]
=> ? = 2 - 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 = 2 - 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]
=> ? = 1 - 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]
=> ? = 1 - 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]
=> ? = 1 - 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 = 2 - 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 = 2 - 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]
=> ? = 2 - 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]
=> ? = 1 - 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 = 2 - 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]
=> ? = 1 - 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]
=> ? = 2 - 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]
=> ? = 1 - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 1 = 2 - 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 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]
=> ? = 1 - 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 = 2 - 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 1 = 2 - 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 = 2 - 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 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]
=> ? = 1 - 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 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]
=> ? = 1 - 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 = 2 - 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 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]
=> ? = 1 - 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]
=> ? = 1 - 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]
=> ? = 2 - 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 1 = 2 - 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 = 2 - 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 = 2 - 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 1 = 2 - 1
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 1 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 1
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 1 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 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 = 2 - 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [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 = 2 - 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [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 = 2 - 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [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 = 2 - 1
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001498
(load all 3 compositions to match this statistic)
(load all 3 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: 30% ●values known / values provided: 30%●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: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 50%
Values
[1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 1 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 1 - 2
[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 = 2 - 2
[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]
=> ? = 1 - 2
[1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 2
[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]
=> ? = 2 - 2
[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 = 2 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[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 = 2 - 2
[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]
=> ? = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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]
=> ? = 2 - 2
[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 = 2 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 1 - 2
[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 = 2 - 2
[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 = 2 - 2
[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]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[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 = 2 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> 0 = 2 - 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[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 = 2 - 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 0 = 2 - 2
[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 = 2 - 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[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 = 2 - 2
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 1 - 2
[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]
=> ? = 2 - 2
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1 - 2
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> 0 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> 0 = 2 - 2
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 0 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[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 = 2 - 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [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 = 2 - 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [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 = 2 - 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [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 = 2 - 2
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: St001198
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 50%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001198: Dyck paths ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 50%
Values
[1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 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]
=> ? = 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]
=> ? = 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]
=> ? = 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]
=> [1,1,0,0,1,1,0,0]
=> 2
[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]
=> ? = 1
[1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 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]
=> ? = 2
[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]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[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]
=> ? = 2
[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]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,0,0,1,0,1,1,0,0]
=> 2
[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]
=> ? = 2
[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]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[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]
=> ? = 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]
=> ? = 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]
=> ? = 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]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[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]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 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]
=> ? = 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]
=> ? = 2
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
Description
The number of simple modules in the algebra $eAe$ with projective dimension at most 1 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Matching statistic: St001206
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 50%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
St001206: Dyck paths ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 50%
Values
[1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> ? = 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]
=> ? = 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]
=> ? = 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]
=> ? = 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]
=> [1,1,0,0,1,1,0,0]
=> 2
[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]
=> ? = 1
[1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 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]
=> ? = 2
[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]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[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]
=> ? = 2
[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]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,0,0,1,0,1,1,0,0]
=> 2
[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]
=> ? = 2
[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]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[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]
=> ? = 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]
=> ? = 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]
=> ? = 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]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,0,0,0]
=> 2
[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]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[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]
=> ? = 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]
=> ? = 2
[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]
=> ? = 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 2
[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]
=> ? = 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]
=> ? = 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]
=> ? = 2
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,1,0,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[1,1,0,0,1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 2
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 2
[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]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 2
[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]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> 2
Description
The maximal dimension of an indecomposable projective $eAe$-module (that is the height of the corresponding Dyck path) of the corresponding Nakayama algebra with minimal faithful projective-injective module $eA$.
Matching statistic: St001884
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001884: Binary words ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 100%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001884: Binary words ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 100%
Values
[1,1,1,0,0,0]
=> []
=> []
=> => ? = 1
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 1
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 1
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 1
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 1
[1,1,1,1,0,0,0,0]
=> []
=> []
=> => ? = 2
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => ? = 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => ? = 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1010110100 => ? = 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => ? = 2
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => ? = 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => ? = 2
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> 1011010100 => ? = 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1011011000 => ? = 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1011101000 => ? = 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => ? = 2
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => ? = 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => ? = 2
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => ? = 2
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> 1100110100 => ? = 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => ? = 2
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,1,0,1,0,0,1,0,1,0]
=> 1101001010 => ? = 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> 1101001100 => ? = 2
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> 1101010010 => ? = 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1110001010 => ? = 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => ? = 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1110010010 => ? = 2
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 1
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1110100010 => ? = 1
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1111000010 => ? = 2
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 1
[1,1,1,1,1,0,0,0,0,0]
=> []
=> []
=> => ? = 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> 101010101010 => ? = 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> 101010101100 => ? = 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> 101010110010 => ? = 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> 101010110100 => ? = 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> 101010111000 => ? = 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 101011001100 => ? = 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> 101011010010 => ? = 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> 101011010100 => ? = 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> 101011011000 => ? = 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> 101011100010 => ? = 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> 101011100100 => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> 101011101000 => ? = 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 101011110000 => ? = 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> 101100101010 => ? = 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> 101100101100 => ? = 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 101100110010 => ? = 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> 101100110100 => ? = 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 101100111000 => ? = 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 101101001010 => ? = 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> 101101001100 => ? = 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> 101101010100 => ? = 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 101101011000 => ? = 2
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> 101101100010 => ? = 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> 101101100100 => ? = 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 1
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 1
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 1
Description
The number of borders of a binary word.
A border of a binary word $w$ is a word which is both a prefix and a suffix of $w$.
Matching statistic: St000186
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000186: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 100%
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00082: Standard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000186: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 100%
Values
[1,1,1,0,0,0]
=> []
=> []
=> ?
=> ? = 1 + 2
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [[1,3],[2,5],[4]]
=> [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 3 = 1 + 2
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [[1,2,5],[3,4]]
=> [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 1 + 2
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> 4 = 2 + 2
[1,1,1,0,0,0,1,0]
=> [3]
=> [[1,2,3]]
=> [[3,0,0],[2,0],[1]]
=> 3 = 1 + 2
[1,1,1,1,0,0,0,0]
=> []
=> []
=> ?
=> ? = 2 + 2
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [[1,3,6],[2,5,9],[4,8],[7]]
=> [[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [[1,3,8,9],[2,5],[4,7],[6]]
=> [[4,2,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [[1,3,8],[2,5],[4,7],[6]]
=> [[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [[1,3],[2,5],[4,7],[6]]
=> [[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [[1,4,5,9],[2,7,8],[3],[6]]
=> [[4,3,1,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [[1,4,5],[2,7,8],[3],[6]]
=> [[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [[1,4,7],[2,6],[3],[5]]
=> [[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [[1,4],[2,6],[3],[5]]
=> [[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [[1,5],[2],[3],[4]]
=> [[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> 4 = 2 + 2
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [[1,2,5,9],[3,4,8],[6,7]]
=> [[4,3,2,0,0,0,0,0,0],[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 1 + 2
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [[1,2,5],[3,4,8],[6,7]]
=> [[3,3,2,0,0,0,0,0],[3,2,2,0,0,0,0],[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 2 + 2
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [[1,2,7,8],[3,4],[5,6]]
=> [[4,2,2,0,0,0,0,0],[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 2 + 2
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [[1,2,7],[3,4],[5,6]]
=> [[3,2,2,0,0,0,0],[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 2 + 2
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 2 + 2
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [[1,3,4,8],[2,6,7],[5]]
=> [[4,3,1,0,0,0,0,0],[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [[1,3,4],[2,6,7],[5]]
=> [[3,3,1,0,0,0,0],[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [[1,3,6,7],[2,5],[4]]
=> [[4,2,1,0,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [[1,3],[2,5],[4]]
=> [[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 3 = 1 + 2
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [[1,2,3,7],[4,5,6]]
=> [[4,3,0,0,0,0,0],[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
=> ? = 2 + 2
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [[1,2,3],[4,5,6]]
=> [[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]]
=> ? = 2 + 2
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [[1,2,5,6],[3,4]]
=> [[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 2 + 2
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [[1,2,5],[3,4]]
=> [[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]]
=> ? = 1 + 2
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> 4 = 2 + 2
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [[1,3,4,5],[2]]
=> [[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [[1,2,3,4]]
=> [[4,0,0,0],[3,0,0],[2,0],[1]]
=> 4 = 2 + 2
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [[1,2,3]]
=> [[3,0,0],[2,0],[1]]
=> 3 = 1 + 2
[1,1,1,1,1,0,0,0,0,0]
=> []
=> []
=> ?
=> ? = 1 + 2
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [[1,3,6,10,15],[2,5,9,14],[4,8,13],[7,12],[11]]
=> [[5,4,3,2,1,0,0,0,0,0,0,0,0,0,0],[4,4,3,2,1,0,0,0,0,0,0,0,0,0],[4,3,3,2,1,0,0,0,0,0,0,0,0],[4,3,2,2,1,0,0,0,0,0,0,0],[4,3,2,1,1,0,0,0,0,0,0],[4,3,2,1,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [[1,3,6,10],[2,5,9,14],[4,8,13],[7,12],[11]]
=> [[4,4,3,2,1,0,0,0,0,0,0,0,0,0],[4,3,3,2,1,0,0,0,0,0,0,0,0],[4,3,2,2,1,0,0,0,0,0,0,0],[4,3,2,1,1,0,0,0,0,0,0],[4,3,2,1,0,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [[1,3,6,13,14],[2,5,9],[4,8,12],[7,11],[10]]
=> [[5,3,3,2,1,0,0,0,0,0,0,0,0,0],[4,3,3,2,1,0,0,0,0,0,0,0,0],[3,3,3,2,1,0,0,0,0,0,0,0],[3,3,2,2,1,0,0,0,0,0,0],[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [[1,3,6,13],[2,5,9],[4,8,12],[7,11],[10]]
=> [[4,3,3,2,1,0,0,0,0,0,0,0,0],[3,3,3,2,1,0,0,0,0,0,0,0],[3,3,2,2,1,0,0,0,0,0,0],[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]]
=> [[3,3,3,2,1,0,0,0,0,0,0,0],[3,3,2,2,1,0,0,0,0,0,0],[3,3,2,1,1,0,0,0,0,0],[3,3,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[3,2,1,1,0,0,0],[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [[1,3,8,9],[2,5,12,13],[4,7],[6,11],[10]]
=> [[4,4,2,2,1,0,0,0,0,0,0,0,0],[4,3,2,2,1,0,0,0,0,0,0,0],[4,2,2,2,1,0,0,0,0,0,0],[4,2,2,1,1,0,0,0,0,0],[4,2,2,1,0,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> [[1,3,8,12,13],[2,5,11],[4,7],[6,10],[9]]
=> [[5,3,2,2,1,0,0,0,0,0,0,0,0],[4,3,2,2,1,0,0,0,0,0,0,0],[3,3,2,2,1,0,0,0,0,0,0],[3,2,2,2,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]]
=> [[4,3,2,2,1,0,0,0,0,0,0,0],[3,3,2,2,1,0,0,0,0,0,0],[3,2,2,2,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> [[1,3,8],[2,5,11],[4,7],[6,10],[9]]
=> [[3,3,2,2,1,0,0,0,0,0,0],[3,2,2,2,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,2,1,0,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> [[1,3,10,11,12],[2,5],[4,7],[6,9],[8]]
=> [[5,2,2,2,1,0,0,0,0,0,0,0],[4,2,2,2,1,0,0,0,0,0,0],[3,2,2,2,1,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> [[1,3,10,11],[2,5],[4,7],[6,9],[8]]
=> [[4,2,2,2,1,0,0,0,0,0,0],[3,2,2,2,1,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> [[1,3,10],[2,5],[4,7],[6,9],[8]]
=> [[3,2,2,2,1,0,0,0,0,0],[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2,1]
=> [[1,3],[2,5],[4,7],[6,9],[8]]
=> [[2,2,2,2,1,0,0,0,0],[2,2,2,1,1,0,0,0],[2,2,2,1,0,0,0],[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> [[1,4,5,9,14],[2,7,8,13],[3,11,12],[6],[10]]
=> [[5,4,3,1,1,0,0,0,0,0,0,0,0,0],[4,4,3,1,1,0,0,0,0,0,0,0,0],[4,3,3,1,1,0,0,0,0,0,0,0],[4,3,2,1,1,0,0,0,0,0,0],[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [[1,4,5,9],[2,7,8,13],[3,11,12],[6],[10]]
=> [[4,4,3,1,1,0,0,0,0,0,0,0,0],[4,3,3,1,1,0,0,0,0,0,0,0],[4,3,2,1,1,0,0,0,0,0,0],[4,3,1,1,1,0,0,0,0,0],[4,3,1,1,0,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [[1,4,5,12,13],[2,7,8],[3,10,11],[6],[9]]
=> [[5,3,3,1,1,0,0,0,0,0,0,0,0],[4,3,3,1,1,0,0,0,0,0,0,0],[3,3,3,1,1,0,0,0,0,0,0],[3,3,2,1,1,0,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]]
=> [[4,3,3,1,1,0,0,0,0,0,0,0],[3,3,3,1,1,0,0,0,0,0,0],[3,3,2,1,1,0,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [[1,4,5],[2,7,8],[3,10,11],[6],[9]]
=> [[3,3,3,1,1,0,0,0,0,0,0],[3,3,2,1,1,0,0,0,0,0],[3,3,1,1,1,0,0,0,0],[3,3,1,1,0,0,0,0],[3,2,1,1,0,0,0],[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> [[1,4,7,8,13],[2,6,11,12],[3,10],[5],[9]]
=> [[5,4,2,1,1,0,0,0,0,0,0,0,0],[4,4,2,1,1,0,0,0,0,0,0,0],[4,3,2,1,1,0,0,0,0,0,0],[4,2,2,1,1,0,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]]
=> [[4,4,2,1,1,0,0,0,0,0,0,0],[4,3,2,1,1,0,0,0,0,0,0],[4,2,2,1,1,0,0,0,0,0],[4,2,1,1,1,0,0,0,0],[4,2,1,1,0,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> [[1,4,7,11],[2,6,10],[3,9],[5],[8]]
=> [[4,3,2,1,1,0,0,0,0,0,0],[3,3,2,1,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 1 + 2
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> [[1,4,7],[2,6,10],[3,9],[5],[8]]
=> [[3,3,2,1,1,0,0,0,0,0],[3,2,2,1,1,0,0,0,0],[3,2,1,1,1,0,0,0],[3,2,1,1,0,0,0],[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]]
=> ? = 2 + 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> 4 = 2 + 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 3 = 1 + 2
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> 4 = 2 + 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [4]
=> [[1,2,3,4]]
=> [[4,0,0,0],[3,0,0],[2,0],[1]]
=> 4 = 2 + 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> [[1,2,3]]
=> [[3,0,0],[2,0],[1]]
=> 3 = 1 + 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> 4 = 2 + 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,1,1]
=> [[1],[2],[3]]
=> [[1,1,1],[1,1],[1]]
=> 3 = 1 + 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [2,2]
=> [[1,2],[3,4]]
=> [[2,2,0,0],[2,1,0],[2,0],[1]]
=> 4 = 2 + 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> [4]
=> [[1,2,3,4]]
=> [[4,0,0,0],[3,0,0],[2,0],[1]]
=> 4 = 2 + 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [3]
=> [[1,2,3]]
=> [[3,0,0],[2,0],[1]]
=> 3 = 1 + 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]
=> [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [[1,1,1,1],[1,1,1],[1,1],[1]]
=> 4 = 2 + 2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]
=> [4]
=> [[1,2,3,4]]
=> [[4,0,0,0],[3,0,0],[2,0],[1]]
=> 4 = 2 + 2
Description
The sum of the first row in a Gelfand-Tsetlin pattern.
Matching statistic: St001416
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001416: Binary words ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 100%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001416: Binary words ⟶ ℤResult quality: 4% ●values known / values provided: 4%●distinct values known / distinct values provided: 100%
Values
[1,1,1,0,0,0]
=> []
=> []
=> => ? = 1 + 4
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5 = 1 + 4
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 5 = 1 + 4
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5 = 1 + 4
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 6 = 2 + 4
[1,1,1,0,0,0,1,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 5 = 1 + 4
[1,1,1,1,0,0,0,0]
=> []
=> []
=> => ? = 2 + 4
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0]
=> 1010101100 => ? = 1 + 4
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,0]
=> 1010110010 => ? = 1 + 4
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0]
=> 1010110100 => ? = 2 + 4
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0]
=> 1010111000 => ? = 2 + 4
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0]
=> 1011001010 => ? = 1 + 4
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0]
=> 1011001100 => ? = 2 + 4
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,0]
=> 1011010100 => ? = 1 + 4
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0]
=> 1011011000 => ? = 2 + 4
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [1,0,1,1,1,0,1,0,0,0]
=> 1011101000 => ? = 1 + 4
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 1011110000 => ? = 2 + 4
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1100101010 => ? = 1 + 4
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [1,1,0,0,1,0,1,1,0,0]
=> 1100101100 => ? = 2 + 4
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [1,1,0,0,1,1,0,0,1,0]
=> 1100110010 => ? = 2 + 4
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [1,1,0,0,1,1,0,1,0,0]
=> 1100110100 => ? = 2 + 4
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1100111000 => ? = 2 + 4
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [1,1,0,1,0,0,1,0,1,0]
=> 1101001010 => ? = 2 + 4
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [1,1,0,1,0,0,1,1,0,0]
=> 1101001100 => ? = 2 + 4
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [1,1,0,1,0,1,0,0,1,0]
=> 1101010010 => ? = 1 + 4
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5 = 1 + 4
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 5 = 1 + 4
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [1,1,1,0,0,0,1,0,1,0]
=> 1110001010 => ? = 2 + 4
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> 1110001100 => ? = 2 + 4
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [1,1,1,0,0,1,0,0,1,0]
=> 1110010010 => ? = 2 + 4
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5 = 1 + 4
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 6 = 2 + 4
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [1,1,1,0,1,0,0,0,1,0]
=> 1110100010 => ? = 1 + 4
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1111000010 => ? = 2 + 4
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 5 = 1 + 4
[1,1,1,1,1,0,0,0,0,0]
=> []
=> []
=> => ? = 1 + 4
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> 101010101010 => ? = 1 + 4
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> 101010101100 => ? = 2 + 4
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> 101010110010 => ? = 2 + 4
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> 101010110100 => ? = 1 + 4
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> 101010111000 => ? = 2 + 4
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> 101011001100 => ? = 1 + 4
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> 101011010010 => ? = 1 + 4
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> 101011010100 => ? = 2 + 4
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> 101011011000 => ? = 2 + 4
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> 101011100010 => ? = 2 + 4
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> 101011100100 => ? = 1 + 4
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [3,2,2,2,1]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> 101011101000 => ? = 2 + 4
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,2,2,2,1]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> 101011110000 => ? = 2 + 4
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> 101100101010 => ? = 2 + 4
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> 101100101100 => ? = 1 + 4
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 101100110010 => ? = 2 + 4
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> 101100110100 => ? = 2 + 4
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> 101100111000 => ? = 2 + 4
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> 101101001010 => ? = 1 + 4
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> 101101001100 => ? = 2 + 4
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> 101101010100 => ? = 1 + 4
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> 101101011000 => ? = 2 + 4
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> 101101100010 => ? = 1 + 4
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> 101101100100 => ? = 2 + 4
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5 = 1 + 4
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 5 = 1 + 4
[1,1,1,1,0,0,1,0,1,0,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5 = 1 + 4
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 6 = 2 + 4
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 5 = 1 + 4
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 10101100 => 5 = 1 + 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 10111000 => 5 = 1 + 4
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 11001010 => 5 = 1 + 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 11001100 => 6 = 2 + 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 11100010 => 5 = 1 + 4
Description
The length of a longest palindromic factor of a binary word.
A factor of a word is a sequence of consecutive letters. This statistic records the maximal length of a palindromic factor.
Sorry, this statistic was not found in the database
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