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Your data matches 10 different statistics following compositions of up to 3 maps.
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Matching statistic: St001232
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1,0]
=> [1,0]
=> [1,0]
=> 0
[1,0,1,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> 1
[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]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 3
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[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]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[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]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[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]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St000264
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 34%●distinct values known / distinct values provided: 14%
Mp00119: Dyck paths —to 321-avoiding permutation (Krattenthaler)⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000264: Graphs ⟶ ℤResult quality: 14% ●values known / values provided: 34%●distinct values known / distinct values provided: 14%
Values
[1,0]
=> [1,0]
=> [1] => ([],1)
=> ? = 0 - 1
[1,0,1,0]
=> [1,1,0,0]
=> [2,1] => ([(0,1)],2)
=> ? = 1 - 1
[1,1,0,0]
=> [1,0,1,0]
=> [1,2] => ([],2)
=> ? = 1 - 1
[1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,2,3,4] => ([],4)
=> ? = 3 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 3 - 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => ([(2,4),(3,4)],5)
=> ? = 3 - 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => ([],5)
=> ? = 2 - 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 5 - 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 5 - 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [2,3,4,6,1,5] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 5 - 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 5 - 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [2,3,4,5,1,6] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 5 - 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 5 - 1
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
=> 4 = 5 - 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,3,4,6,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6)
=> ? = 5 - 1
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,3,4,5,6,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
=> ? = 5 - 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6)
=> ? = 5 - 1
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6)
=> 4 = 5 - 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6)
=> ? = 5 - 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6)
=> ? = 5 - 1
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,2,3,5,6,4] => ([(3,5),(4,5)],6)
=> ? = 5 - 1
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [2,1,3,4,5,6] => ([(4,5)],6)
=> ? = 5 - 1
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,3,2,4,5,6] => ([(4,5)],6)
=> ? = 5 - 1
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,5,6] => ([(4,5)],6)
=> ? = 5 - 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,5,4,6] => ([(4,5)],6)
=> ? = 3 - 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,6,5] => ([(4,5)],6)
=> ? = 5 - 1
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6] => ([],6)
=> ? = 3 - 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [4,5,6,7,1,2,3] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [3,5,6,7,1,2,4] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [3,4,6,7,1,2,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [3,4,5,6,7,1,2] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [3,4,5,6,1,7,2] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [2,5,6,7,1,3,4] => ([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [2,4,6,7,1,3,5] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [2,4,5,6,7,1,3] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [2,4,5,6,1,7,3] => ([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [2,3,6,7,1,4,5] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [2,3,5,6,7,1,4] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [2,3,5,6,1,7,4] => ([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [2,3,4,6,7,1,5] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [3,1,4,5,6,7,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ? = 5 - 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [2,4,1,5,6,7,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 5 - 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [2,3,5,1,6,7,4] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
=> ? = 5 - 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [2,3,4,6,1,7,5] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 6 - 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,6,7,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 3 - 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0,1,0]
=> [3,4,5,6,1,2,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> [2,4,5,6,1,3,7] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> [2,3,5,6,1,4,7] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [2,3,4,5,6,1,7] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=> [2,3,4,5,1,7,6] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,5,6,7,2,3,4] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)
=> 4 = 5 - 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,4,6,7,2,3,5] => ([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,4,5,6,7,2,3] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,4,5,6,2,7,3] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,3,6,7,2,4,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,3,5,6,7,2,4] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,3,5,6,2,7,4] => ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,3,4,6,7,2,5] => ([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=> [2,1,4,5,6,7,3] => ([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,4,2,5,6,7,3] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
=> ? = 5 - 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,3,5,2,6,7,4] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 5 - 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,3,4,6,2,7,5] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 6 - 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,3,4,5,6,7,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 3 - 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0,1,0]
=> [2,3,4,5,1,6,7] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=> [1,4,5,6,2,3,7] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,3,5,6,2,4,7] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,3,4,5,6,2,7] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=> [1,3,4,5,2,7,6] => ([(1,2),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,2,6,7,3,4,5] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,2,5,6,7,3,4] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,2,5,6,3,7,4] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,2,4,6,7,3,5] => ([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
=> 4 = 5 - 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,1,0,1,0,0]
=> [2,1,3,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=> [1,3,2,5,6,7,4] => ([(1,2),(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,2,5,3,6,7,4] => ([(2,6),(3,6),(4,5),(5,6)],7)
=> ? = 5 - 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,2,4,6,3,7,5] => ([(2,6),(3,5),(4,5),(4,6)],7)
=> ? = 6 - 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,2,4,5,6,7,3] => ([(2,6),(3,6),(4,6),(5,6)],7)
=> ? = 3 - 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,2,4,5,6,3,7] => ([(3,6),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,2,3,6,7,4,5] => ([(3,5),(3,6),(4,5),(4,6)],7)
=> 4 = 5 - 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,1,0,0]
=> [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7)
=> ? = 5 - 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,2,3,6,4,7,5] => ([(3,6),(4,5),(5,6)],7)
=> ? = 6 - 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7)
=> ? = 6 - 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7)
=> ? = 4 - 1
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Matching statistic: St001227
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 71%
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
Mp00099: Dyck paths —bounce path⟶ Dyck paths
St001227: Dyck paths ⟶ ℤResult quality: 27% ●values known / values provided: 27%●distinct values known / distinct values provided: 71%
Values
[1,0]
=> [1,0]
=> [1,0]
=> [1,0]
=> 0
[1,0,1,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> 1
[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]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 3
[1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> 3
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> 5
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[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]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[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]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[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]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[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]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> ? = 5
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[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]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=> ? = 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=> ? = 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ? = 3
Description
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
Matching statistic: St001603
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 22%●distinct values known / distinct values provided: 14%
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 14% ●values known / values provided: 22%●distinct values known / distinct values provided: 14%
Values
[1,0]
=> [1] => [1]
=> []
=> ? = 0 - 4
[1,0,1,0]
=> [1,2] => [1,1]
=> [1]
=> ? = 1 - 4
[1,1,0,0]
=> [2,1] => [2]
=> []
=> ? = 1 - 4
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => [4]
=> []
=> ? = 3 - 4
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,1,0,1,1,0,0,0,0]
=> [5,2,4,3,1] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,1,1,1,0,0,0,0,0]
=> [5,4,3,2,1] => [5]
=> []
=> ? = 2 - 4
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,2,6,5,4,3] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,3,6,5,4,2] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,6,3,5,4,2] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,6,4,5,3,2] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,6,5,4,3,2] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,1,6,5,4,3] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,6,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,6,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [2,6,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,6,5,4,3,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [3,2,6,5,4,1] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [6,2,3,5,4,1] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [6,2,4,5,3,1] => [4,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [6,2,5,4,3,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [6,3,5,4,2,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [5,4,3,2,1,6] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [5,4,3,2,6,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [6,4,3,2,5,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [6,4,3,5,2,1] => [5,1]
=> [1]
=> ? = 3 - 4
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [6,5,3,4,2,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [6,5,4,3,2,1] => [6]
=> []
=> ? = 3 - 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,2,3,7,6,5,4] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,2,4,7,6,5,3] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,2,7,4,6,5,3] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,2,7,6,5,4,3] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,3,2,7,6,5,4] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,4,7,6,5,2] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,3,7,4,6,5,2] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,3,7,6,5,4,2] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,3,7,6,5,2] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,7,3,4,6,5,2] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,7,3,6,5,4,2] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,7,4,3,6,5,2] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,7,4,6,5,3,2] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,6,5,4,3,2,7] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,6,5,4,3,7,2] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,7,5,4,3,6,2] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,7,5,4,6,3,2] => [5,1,1]
=> [1,1]
=> ? = 6 - 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,7,6,5,4,3,2] => [6,1]
=> [1]
=> ? = 3 - 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [2,1,3,7,6,5,4] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [2,1,4,7,6,5,3] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [2,1,7,4,6,5,3] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [2,1,7,6,5,4,3] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [2,3,1,7,6,5,4] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,4,7,6,5,1] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [2,3,7,4,6,5,1] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,7,6,5,4,1] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [2,4,3,7,6,5,1] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [2,7,3,4,6,5,1] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [2,7,3,6,5,4,1] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [2,7,4,3,6,5,1] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [2,7,4,6,5,3,1] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=> [2,6,5,4,3,1,7] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [2,6,5,4,3,7,1] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [2,7,5,4,3,6,1] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [2,7,5,4,6,3,1] => [5,1,1]
=> [1,1]
=> ? = 6 - 4
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [2,7,6,5,4,3,1] => [6,1]
=> [1]
=> ? = 3 - 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [3,2,1,7,6,5,4] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [3,2,4,7,6,5,1] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [3,2,7,4,6,5,1] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [3,2,7,6,5,4,1] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [4,2,3,7,6,5,1] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [7,2,3,4,6,5,1] => [4,1,1,1]
=> [1,1,1]
=> 1 = 5 - 4
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=> [7,2,3,6,5,4,1] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [7,2,4,3,6,5,1] => [4,2,1]
=> [2,1]
=> 1 = 5 - 4
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [7,2,4,6,5,3,1] => [5,1,1]
=> [1,1]
=> ? = 5 - 4
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
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
[1,0]
=> [1] => [1]
=> []
=> ? = 0 - 4
[1,0,1,0]
=> [2,1] => [1,1]
=> [1]
=> ? = 1 - 4
[1,1,0,0]
=> [1,2] => [2]
=> []
=> ? = 1 - 4
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4]
=> []
=> ? = 3 - 4
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,1,0,1,1,0,0,0,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5]
=> []
=> ? = 2 - 4
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,5,6,1,3] => [4,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,3,5,6,1,4] => [4,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,3,4,5,1,6] => [5,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,1,2] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,5,6,2,4] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,3,4,6,2,5] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,3,4,5,2,6] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,3,4,5,6,2] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,5,6,2,3] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,2,4,6,3,5] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,2,4,5,3,6] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,2,4,5,6,3] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,2,3,5,6,4] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [6,1,2,3,4,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,6,2,3,4,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,2,6,3,4,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,2,3,6,4,5] => [5,1]
=> [1]
=> ? = 3 - 4
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,2,3,4,6,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => [6]
=> []
=> ? = 3 - 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,6,7,1,3,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,4,5,7,1,3,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,4,5,6,1,3,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,4,5,6,7,1,3] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,5,6,7,1,3,4] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,5,7,1,4,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,3,5,6,1,4,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,5,6,7,1,4] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,3,6,7,1,4,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,3,4,6,1,5,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,3,4,6,7,1,5] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,3,4,7,1,5,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,3,4,5,7,1,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,1,3,4,5,6,7] => [6,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [2,3,1,4,5,6,7] => [6,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [2,3,4,1,5,6,7] => [6,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [2,3,4,5,1,6,7] => [6,1]
=> [1]
=> ? = 6 - 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => [6,1]
=> [1]
=> ? = 3 - 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [3,4,6,7,1,2,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [3,4,5,7,1,2,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [3,4,5,6,1,2,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [3,5,6,7,1,2,4] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,3,5,6,2,4,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,3,5,6,7,2,4] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,3,6,7,2,4,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,3,4,6,2,5,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,3,4,6,7,2,5] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,3,4,7,2,5,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,3,4,5,7,2,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,1,2,3] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,4,5,7,2,3,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,4,6,7,2,3,5] => [4,3]
=> [3]
=> 1 = 5 - 4
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
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001605: Integer partitions ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 14%
Values
[1,0]
=> [1] => [1]
=> []
=> ? = 0 - 4
[1,0,1,0]
=> [2,1] => [1,1]
=> [1]
=> ? = 1 - 4
[1,1,0,0]
=> [1,2] => [2]
=> []
=> ? = 1 - 4
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [4]
=> []
=> ? = 3 - 4
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,0,1,1,1,0,0,0,0]
=> [1,3,4,5,2] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,1,0,1,1,0,0,0,0]
=> [1,2,4,5,3] => [4,1]
=> [1]
=> ? = 3 - 4
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [5]
=> []
=> ? = 2 - 4
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,5,6,1,3] => [4,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,3,5,6,1,4] => [4,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,3,4,6,1,5] => [4,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,3,4,5,1,6] => [5,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,3,4,5,6,1] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,1,2] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,5,6,2,4] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,3,4,6,2,5] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,3,4,5,2,6] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,3,4,5,6,2] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,4,5,6,2,3] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,2,4,6,3,5] => [4,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,2,4,5,3,6] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,2,4,5,6,3] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,2,3,5,6,4] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [6,1,2,3,4,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,6,2,3,4,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,2,6,3,4,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,2,3,6,4,5] => [5,1]
=> [1]
=> ? = 3 - 4
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,2,3,4,6,5] => [5,1]
=> [1]
=> ? = 5 - 4
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,2,3,4,5,6] => [6]
=> []
=> ? = 3 - 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [2,4,6,7,1,3,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,4,5,7,1,3,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,4,5,6,1,3,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [2,4,5,6,7,1,3] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,5,6,7,1,3,4] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [2,3,5,7,1,4,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [2,3,5,6,1,4,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [2,3,5,6,7,1,4] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,3,6,7,1,4,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [2,3,4,6,1,5,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [2,3,4,6,7,1,5] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,3,4,7,1,5,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [2,3,4,5,7,1,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,1,3,4,5,6,7] => [6,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [2,3,1,4,5,6,7] => [6,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [2,3,4,1,5,6,7] => [6,1]
=> [1]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [2,3,4,5,1,6,7] => [6,1]
=> [1]
=> ? = 6 - 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => [6,1]
=> [1]
=> ? = 3 - 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [3,4,6,7,1,2,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [3,4,5,7,1,2,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [3,4,5,6,1,2,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [3,4,5,6,7,1,2] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [3,5,6,7,1,2,4] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,3,5,7,2,4,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,3,5,6,2,4,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,3,5,6,7,2,4] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,3,6,7,2,4,5] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,3,4,6,2,5,7] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,3,4,6,7,2,5] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,3,4,7,2,5,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=> [1,3,4,5,7,2,6] => [5,2]
=> [2]
=> ? = 5 - 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=> [4,5,6,7,1,2,3] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,4,5,7,2,3,6] => [4,3]
=> [3]
=> 1 = 5 - 4
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,4,6,7,2,3,5] => [4,3]
=> [3]
=> 1 = 5 - 4
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: St001879
Mp00296: Dyck paths —Knuth-Krattenthaler⟶ Dyck paths
Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Values
[1,0]
=> [1,0]
=> [.,.]
=> ([],1)
=> ? = 0 + 1
[1,0,1,0]
=> [1,1,0,0]
=> [[.,.],.]
=> ([(0,1)],2)
=> ? = 1 + 1
[1,1,0,0]
=> [1,0,1,0]
=> [.,[.,.]]
=> ([(0,1)],2)
=> ? = 1 + 1
[1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0]
=> [[.,.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 3 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [[[.,.],.],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? = 3 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [.,[[.,[[.,.],.]],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 3 + 1
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> [[[.,[[.,.],.]],.],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4 = 3 + 1
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[[.,.],.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? = 2 + 1
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [[[.,[.,.]],[.,.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ? = 5 + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ? = 5 + 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [[.,[.,.]],[[.,.],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 5 + 1
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [[[.,.],.],[[.,.],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 5 + 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [[[.,.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ? = 5 + 1
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [.,[[.,.],[.,[.,[.,.]]]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 1
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [.,[[.,.],[[.,.],[.,.]]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ? = 5 + 1
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [.,[.,[.,[[.,.],[.,.]]]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [.,[[.,[[.,.],[.,.]]],.]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 1
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [.,[[.,.],[.,[[.,.],.]]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 1
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [[[.,.],[.,[.,[.,.]]]],.]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 1
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [[.,[.,[[.,.],[.,.]]]],.]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> [[[.,[[.,.],[.,.]]],.],.]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 1
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[[.,.],[.,[[.,.],.]]],.]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 1
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> [[.,[.,.]],[.,[[.,.],.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 1
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [[[[.,.],.],.],[.,[.,.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 1
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [[[.,[.,.]],.],[.,[.,.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 1
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [[[.,.],.],[[.,[.,.]],.]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [[[.,.],.],[.,[.,[.,.]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 3 + 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [[[.,.],.],[.,[[.,.],.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 1
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [[[.,.],[.,[.,.]]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ? = 3 + 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [[[[.,.],.],[.,.]],[[.,.],.]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 5 + 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [[.,[[.,[[.,.],.]],.]],[.,.]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? = 5 + 1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=> [[[[.,[[.,.],.]],.],.],[.,.]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? = 5 + 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> [[[.,[.,.]],[.,.]],[[.,.],.]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 5 + 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=> [[[[.,.],.],[[[.,.],.],.]],.]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [[[[.,[[.,.],.]],.],[.,.]],.]
=> ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
=> ? = 5 + 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [[[[[[.,.],.],[.,.]],.],.],.]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 5 + 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [[[[.,.],.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
=> ? = 5 + 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [[.,[[.,.],.]],[[[.,.],.],.]]
=> ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ? = 5 + 1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [[.,.],[[[[.,.],.],[.,.]],.]]
=> ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
=> ? = 5 + 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [[.,[[.,.],.]],[[.,.],[.,.]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ? = 5 + 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [[[[.,.],.],.],[[[.,.],.],.]]
=> ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ? = 5 + 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=> [[[[.,.],.],.],[[.,.],[.,.]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ? = 5 + 1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [[[.,.],[[.,.],.]],[.,[.,.]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 5 + 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 5 + 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,1,0,0]
=> [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 5 + 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [[[.,.],[[[.,.],.],.]],[.,.]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ? = 6 + 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> [[[.,.],[[.,.],.]],[[.,.],.]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 3 + 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [.,[[[.,.],.],[[.,[.,.]],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 1
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [.,[.,[[.,[[.,[.,.]],.]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [.,[[[.,[[.,[.,.]],.]],.],.]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> [.,[[[.,.],.],[.,[.,[.,.]]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [.,[[[.,.],.],[[[.,.],.],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [.,[[[.,[[.,.],.]],.],[.,.]]]
=> ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
=> ? = 5 + 1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [.,[[[[[.,.],.],[.,.]],.],.]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 5 + 1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [.,[.,[[.,[[[.,.],.],.]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [.,[[[.,[[[.,.],.],.]],.],.]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [[[[.,[[.,[.,.]],.]],.],.],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=> [[.,[[.,[[[.,.],.],.]],.]],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=> [[[[.,[[[.,.],.],.]],.],.],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6 = 5 + 1
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Matching statistic: St001880
Mp00296: Dyck paths —Knuth-Krattenthaler⟶ Dyck paths
Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 29%
Values
[1,0]
=> [1,0]
=> [.,.]
=> ([],1)
=> ? = 0 + 2
[1,0,1,0]
=> [1,1,0,0]
=> [[.,.],.]
=> ([(0,1)],2)
=> ? = 1 + 2
[1,1,0,0]
=> [1,0,1,0]
=> [.,[.,.]]
=> ([(0,1)],2)
=> ? = 1 + 2
[1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0]
=> [[.,.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,3)],4)
=> ? = 3 + 2
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [[[.,.],.],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? = 3 + 2
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [.,[[.,[[.,.],.]],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> [[[.,[[.,.],.]],.],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5 = 3 + 2
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [[[.,.],.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> ? = 2 + 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [[[.,[.,.]],[.,.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ? = 5 + 2
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[[.,.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ? = 5 + 2
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [[.,[.,.]],[[.,.],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 5 + 2
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [[[.,.],.],[[.,.],[.,.]]]
=> ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
=> ? = 5 + 2
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [[[.,.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ? = 5 + 2
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [.,[[.,.],[.,[.,[.,.]]]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 2
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [.,[[.,.],[[.,.],[.,.]]]]
=> ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
=> ? = 5 + 2
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [.,[.,[.,[[.,.],[.,.]]]]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 2
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [.,[[.,[[.,.],[.,.]]],.]]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 2
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [.,[[.,.],[.,[[.,.],.]]]]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 2
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> [[[.,.],[.,[.,[.,.]]]],.]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 2
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> [[.,[.,[[.,.],[.,.]]]],.]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 2
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> [[[.,[[.,.],[.,.]]],.],.]
=> ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
=> ? = 5 + 2
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> [[[.,.],[.,[[.,.],.]]],.]
=> ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
=> ? = 5 + 2
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> [[.,[.,.]],[.,[[.,.],.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 2
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [[[[.,.],.],.],[.,[.,.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 2
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0]
=> [[[.,[.,.]],.],[.,[.,.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 2
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0]
=> [[[.,.],.],[[.,[.,.]],.]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 2
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0]
=> [[[.,.],.],[.,[.,[.,.]]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 3 + 2
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,1,0,0]
=> [[[.,.],.],[.,[[.,.],.]]]
=> ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
=> ? = 5 + 2
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [[[.,.],[.,[.,.]]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
=> ? = 3 + 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [[[[.,.],.],[.,.]],[[.,.],.]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 5 + 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [[.,[[.,[[.,.],.]],.]],[.,.]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? = 5 + 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=> [[[[.,[[.,.],.]],.],.],[.,.]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? = 5 + 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> [[[.,[.,.]],[.,.]],[[.,.],.]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 5 + 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=> [[[[.,.],.],[[[.,.],.],.]],.]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [[[[.,[[.,.],.]],.],[.,.]],.]
=> ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
=> ? = 5 + 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [[[[[[.,.],.],[.,.]],.],.],.]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 5 + 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [[[[.,.],.],[[.,.],[.,.]]],.]
=> ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
=> ? = 5 + 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=> [[.,[[.,.],.]],[[[.,.],.],.]]
=> ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ? = 5 + 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [[.,.],[[[[.,.],.],[.,.]],.]]
=> ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
=> ? = 5 + 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=> [[.,[[.,.],.]],[[.,.],[.,.]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ? = 5 + 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=> [[[[.,.],.],.],[[[.,.],.],.]]
=> ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ? = 5 + 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=> [[[[.,.],.],.],[[.,.],[.,.]]]
=> ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
=> ? = 5 + 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [[[.,.],[[.,.],.]],[.,[.,.]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 5 + 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=> [[[[.,.],.],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 5 + 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,1,0,0]
=> [[[.,[.,.]],[[.,.],.]],[.,.]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 5 + 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=> [[[.,.],[[[.,.],.],.]],[.,.]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ? = 6 + 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> [[[.,.],[[.,.],.]],[[.,.],.]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 3 + 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=> [.,[[[.,.],.],[[.,[.,.]],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [.,[.,[[.,[[.,[.,.]],.]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [.,[[[.,[[.,[.,.]],.]],.],.]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> [.,[[[.,.],.],[.,[.,[.,.]]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=> [.,[[[.,.],.],[[[.,.],.],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 5 + 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [.,[[[.,[[.,.],.]],.],[.,.]]]
=> ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
=> ? = 5 + 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [.,[[[[[.,.],.],[.,.]],.],.]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 5 + 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [.,[.,[[.,[[[.,.],.],.]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=> [.,[[[.,[[[.,.],.],.]],.],.]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=> [[[[.,[[.,[.,.]],.]],.],.],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=> [[.,[[.,[[[.,.],.],.]],.]],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=> [[[[.,[[[.,.],.],.]],.],.],.]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 7 = 5 + 2
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001498
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001498: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%
Values
[1,0]
=> [1,0]
=> [1,0]
=> [1,0]
=> ? = 0 - 3
[1,0,1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? = 1 - 3
[1,1,0,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? = 1 - 3
[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]
=> ? = 3 - 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> ? = 3 - 3
[1,1,0,1,1,1,0,0,0,0]
=> [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]
=> ? = 3 - 3
[1,1,1,0,1,1,0,0,0,0]
=> [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]
=> ? = 3 - 3
[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]
=> ? = 2 - 3
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 3 - 3
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 3 - 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> 2 = 5 - 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> 2 = 5 - 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> 2 = 5 - 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> 2 = 5 - 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> 2 = 5 - 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> 2 = 5 - 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 6 - 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 3 - 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> 2 = 5 - 3
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> 2 = 5 - 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> 2 = 5 - 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=> 2 = 5 - 3
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 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%
Mp00103: Dyck paths —peeling map⟶ Dyck paths
Mp00120: Dyck paths —Lalanne-Kreweras involution⟶ Dyck paths
St001199: Dyck paths ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 14%
Values
[1,0]
=> [1,0]
=> [1,0]
=> [1,0]
=> ? = 0 - 4
[1,0,1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? = 1 - 4
[1,1,0,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> ? = 1 - 4
[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]
=> ? = 3 - 4
[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]
=> ? = 3 - 4
[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]
=> ? = 3 - 4
[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]
=> ? = 3 - 4
[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]
=> ? = 2 - 4
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [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]
=> ? = 5 - 4
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [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]
=> ? = 5 - 4
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 3 - 4
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 3 - 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> 1 = 5 - 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=> 1 = 5 - 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> 1 = 5 - 4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=> 1 = 5 - 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> 1 = 5 - 4
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> 1 = 5 - 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 6 - 4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 3 - 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=> 1 = 5 - 4
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> 1 = 5 - 4
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> 1 = 5 - 4
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> ? = 5 - 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> 1 = 5 - 4
Description
The dominant dimension of $eAe$ for the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
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