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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St001019
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
St001019: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> 1
[1,0,1,0]
=> 3
[1,1,0,0]
=> 2
[1,0,1,0,1,0]
=> 6
[1,0,1,1,0,0]
=> 4
[1,1,0,0,1,0]
=> 4
[1,1,0,1,0,0]
=> 4
[1,1,1,0,0,0]
=> 3
[1,0,1,0,1,0,1,0]
=> 10
[1,0,1,0,1,1,0,0]
=> 7
[1,0,1,1,0,0,1,0]
=> 6
[1,0,1,1,0,1,0,0]
=> 7
[1,0,1,1,1,0,0,0]
=> 5
[1,1,0,0,1,0,1,0]
=> 7
[1,1,0,0,1,1,0,0]
=> 5
[1,1,0,1,0,0,1,0]
=> 7
[1,1,0,1,0,1,0,0]
=> 7
[1,1,0,1,1,0,0,0]
=> 5
[1,1,1,0,0,0,1,0]
=> 5
[1,1,1,0,0,1,0,0]
=> 5
[1,1,1,0,1,0,0,0]
=> 5
[1,1,1,1,0,0,0,0]
=> 4
[1,0,1,0,1,0,1,0,1,0]
=> 15
[1,0,1,0,1,0,1,1,0,0]
=> 11
[1,0,1,0,1,1,0,0,1,0]
=> 9
[1,0,1,0,1,1,0,1,0,0]
=> 11
[1,0,1,0,1,1,1,0,0,0]
=> 8
[1,0,1,1,0,0,1,0,1,0]
=> 9
[1,0,1,1,0,0,1,1,0,0]
=> 7
[1,0,1,1,0,1,0,0,1,0]
=> 11
[1,0,1,1,0,1,0,1,0,0]
=> 11
[1,0,1,1,0,1,1,0,0,0]
=> 8
[1,0,1,1,1,0,0,0,1,0]
=> 7
[1,0,1,1,1,0,0,1,0,0]
=> 7
[1,0,1,1,1,0,1,0,0,0]
=> 8
[1,0,1,1,1,1,0,0,0,0]
=> 6
[1,1,0,0,1,0,1,0,1,0]
=> 11
[1,1,0,0,1,0,1,1,0,0]
=> 8
[1,1,0,0,1,1,0,0,1,0]
=> 7
[1,1,0,0,1,1,0,1,0,0]
=> 8
[1,1,0,0,1,1,1,0,0,0]
=> 6
[1,1,0,1,0,0,1,0,1,0]
=> 11
[1,1,0,1,0,0,1,1,0,0]
=> 8
[1,1,0,1,0,1,0,0,1,0]
=> 11
[1,1,0,1,0,1,0,1,0,0]
=> 10
[1,1,0,1,0,1,1,0,0,0]
=> 8
[1,1,0,1,1,0,0,0,1,0]
=> 7
[1,1,0,1,1,0,0,1,0,0]
=> 8
[1,1,0,1,1,0,1,0,0,0]
=> 8
[1,1,0,1,1,1,0,0,0,0]
=> 6
Description
Sum of the projective dimensions of the simple modules in the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001879
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 59%
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00242: Dyck paths —Hessenberg poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 15% ●values known / values provided: 15%●distinct values known / distinct values provided: 59%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> ([(0,1)],2)
=> ? = 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,1,0,0,1,0]
=> ([(0,1),(0,2)],3)
=> ? = 3
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ([(0,2),(2,1)],3)
=> 2
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ? ∊ {4,4,6}
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {4,4,6}
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,0]
=> ([(0,3),(3,1),(3,2)],4)
=> ? ∊ {4,4,6}
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ([(0,3),(2,1),(3,2)],4)
=> 3
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(4,1),(4,2)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(4,2),(4,3)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[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]
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 5
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 6
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 5
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(3,2),(4,1),(4,3)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(3,4),(4,1),(4,2)],5)
=> ? ∊ {5,5,5,5,7,7,7,7,7,10}
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 4
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0,1,0]
=> ([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(5,2),(5,3),(5,4)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)
=> 10
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,0,1,0,0,1,0,1,0]
=> ([(0,5),(4,2),(4,3),(5,1),(5,4)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(4,2),(4,3),(5,4)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
=> 6
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> ([(0,5),(1,2),(2,5),(5,3),(5,4)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)
=> 7
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,1,0,0]
=> ([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> ([(0,5),(1,5),(4,2),(5,3),(5,4)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> ([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)
=> 6
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 7
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)
=> 7
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)
=> 6
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> ([(0,4),(3,2),(4,5),(5,1),(5,3)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(3,5),(4,3),(5,1),(5,2)],6)
=> ? ∊ {6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,11,11,11,11,11,11,11,15}
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 5
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=> ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=> ([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)
=> 11
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)
=> 11
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=> ([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)
=> 11
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
=> 7
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=> ([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)
=> 12
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> ([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)
=> 8
[1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)
=> 8
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)
=> 7
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
=> 8
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> ([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)
=> 8
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)
=> 7
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)
=> 8
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> ([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)
=> 8
[1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> ([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)
=> 7
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> 6
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: St000336
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
St000336: Standard tableaux ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 65%
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
St000336: Standard tableaux ⟶ ℤResult quality: 14% ●values known / values provided: 14%●distinct values known / distinct values provided: 65%
Values
[1,0]
=> [(1,2)]
=> [2,1] => [[1],[2]]
=> 1
[1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => [[1,3],[2,4]]
=> 2
[1,1,0,0]
=> [(1,4),(2,3)]
=> [3,4,2,1] => [[1,4],[2],[3]]
=> 3
[1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => [[1,3,5],[2,4,6]]
=> 3
[1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,5,6,4,3] => [[1,3,6],[2,4],[5]]
=> 4
[1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [3,4,2,1,6,5] => [[1,4,5],[2,6],[3]]
=> 4
[1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> [3,5,2,6,4,1] => [[1,4,6],[2,5],[3]]
=> 4
[1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> [4,5,6,3,2,1] => [[1,5,6],[2],[3],[4]]
=> 6
[1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]]
=> 4
[1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,7,8,6,5] => [[1,3,5,8],[2,4,6],[7]]
=> 5
[1,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8)]
=> [2,1,5,6,4,3,8,7] => [[1,3,6,7],[2,4,8],[5]]
=> 5
[1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,5,7,4,8,6,3] => [[1,3,6,8],[2,4,7],[5]]
=> 5
[1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,6,7,8,5,4,3] => [[1,3,7,8],[2,4],[5],[6]]
=> 7
[1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [3,4,2,1,6,5,8,7] => [[1,4,5,7],[2,6,8],[3]]
=> 5
[1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [3,4,2,1,7,8,6,5] => [[1,4,5,8],[2,6],[3,7]]
=> 6
[1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [3,5,2,6,4,1,8,7] => [[1,4,6,7],[2,5,8],[3]]
=> 5
[1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> [3,5,2,7,4,8,6,1] => [[1,4,6,8],[2,5,7],[3]]
=> 5
[1,1,0,1,1,0,0,0]
=> [(1,8),(2,3),(4,7),(5,6)]
=> [3,6,2,7,8,5,4,1] => [[1,4,7,8],[2,5],[3],[6]]
=> 7
[1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [4,5,6,3,2,1,8,7] => [[1,5,6,7],[2,8],[3],[4]]
=> 7
[1,1,1,0,0,1,0,0]
=> [(1,8),(2,5),(3,4),(6,7)]
=> [4,5,7,3,2,8,6,1] => [[1,5,6,8],[2,7],[3],[4]]
=> 7
[1,1,1,0,1,0,0,0]
=> [(1,8),(2,7),(3,4),(5,6)]
=> [4,6,7,3,8,5,2,1] => [[1,5,7,8],[2,6],[3],[4]]
=> 7
[1,1,1,1,0,0,0,0]
=> [(1,8),(2,7),(3,6),(4,5)]
=> [5,6,7,8,4,3,2,1] => [[1,6,7,8],[2],[3],[4],[5]]
=> 10
[1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10)]
=> [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]]
=> 5
[1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9)]
=> [2,1,4,3,6,5,9,10,8,7] => [[1,3,5,7,10],[2,4,6,8],[9]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10)]
=> [2,1,4,3,7,8,6,5,10,9] => [[1,3,5,8,9],[2,4,6,10],[7]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,10),(6,7),(8,9)]
=> [2,1,4,3,7,9,6,10,8,5] => [[1,3,5,8,10],[2,4,6,9],[7]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,10),(6,9),(7,8)]
=> [2,1,4,3,8,9,10,7,6,5] => [[1,3,5,9,10],[2,4,6],[7],[8]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10)]
=> [2,1,5,6,4,3,8,7,10,9] => [[1,3,6,7,9],[2,4,8,10],[5]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,0,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,10),(8,9)]
=> [2,1,5,6,4,3,9,10,8,7] => [[1,3,6,7,10],[2,4,8],[5,9]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,0,1,0,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10)]
=> [2,1,5,7,4,8,6,3,10,9] => [[1,3,6,8,9],[2,4,7,10],[5]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9)]
=> [2,1,5,7,4,9,6,10,8,3] => [[1,3,6,8,10],[2,4,7,9],[5]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,0,1,1,0,0,0]
=> [(1,2),(3,10),(4,5),(6,9),(7,8)]
=> [2,1,5,8,4,9,10,7,6,3] => [[1,3,6,9,10],[2,4,7],[5],[8]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,1,0,0,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10)]
=> [2,1,6,7,8,5,4,3,10,9] => [[1,3,7,8,9],[2,4,10],[5],[6]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,1,0,0,1,0,0]
=> [(1,2),(3,10),(4,7),(5,6),(8,9)]
=> [2,1,6,7,9,5,4,10,8,3] => [[1,3,7,8,10],[2,4,9],[5],[6]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,1,0,1,0,0,0]
=> [(1,2),(3,10),(4,9),(5,6),(7,8)]
=> [2,1,6,8,9,5,10,7,4,3] => [[1,3,7,9,10],[2,4,8],[5],[6]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7)]
=> [2,1,7,8,9,10,6,5,4,3] => [[1,3,8,9,10],[2,4],[5],[6],[7]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,0,1,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8),(9,10)]
=> [3,4,2,1,6,5,8,7,10,9] => [[1,4,5,7,9],[2,6,8,10],[3]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,0,1,0,1,1,0,0]
=> [(1,4),(2,3),(5,6),(7,10),(8,9)]
=> [3,4,2,1,6,5,9,10,8,7] => [[1,4,5,7,10],[2,6,8],[3,9]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,0,1,1,0,0,1,0]
=> [(1,4),(2,3),(5,8),(6,7),(9,10)]
=> [3,4,2,1,7,8,6,5,10,9] => [[1,4,5,8,9],[2,6,10],[3,7]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,0,1,1,0,1,0,0]
=> [(1,4),(2,3),(5,10),(6,7),(8,9)]
=> [3,4,2,1,7,9,6,10,8,5] => [[1,4,5,8,10],[2,6,9],[3,7]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,10),(6,9),(7,8)]
=> [3,4,2,1,8,9,10,7,6,5] => [[1,4,5,9,10],[2,6],[3,7],[8]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,0,0,1,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8),(9,10)]
=> [3,5,2,6,4,1,8,7,10,9] => [[1,4,6,7,9],[2,5,8,10],[3]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,0,0,1,1,0,0]
=> [(1,6),(2,3),(4,5),(7,10),(8,9)]
=> [3,5,2,6,4,1,9,10,8,7] => [[1,4,6,7,10],[2,5,8],[3,9]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,0,1,0,0,1,0]
=> [(1,8),(2,3),(4,5),(6,7),(9,10)]
=> [3,5,2,7,4,8,6,1,10,9] => [[1,4,6,8,9],[2,5,7,10],[3]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,0,1,0,1,0,0]
=> [(1,10),(2,3),(4,5),(6,7),(8,9)]
=> [3,5,2,7,4,9,6,10,8,1] => [[1,4,6,8,10],[2,5,7,9],[3]]
=> 6
[1,1,0,1,0,1,1,0,0,0]
=> [(1,10),(2,3),(4,5),(6,9),(7,8)]
=> [3,5,2,8,4,9,10,7,6,1] => [[1,4,6,9,10],[2,5,7],[3],[8]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,1,0,0,0,1,0]
=> [(1,8),(2,3),(4,7),(5,6),(9,10)]
=> [3,6,2,7,8,5,4,1,10,9] => [[1,4,7,8,9],[2,5,10],[3],[6]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,1,0,0,1,0,0]
=> [(1,10),(2,3),(4,7),(5,6),(8,9)]
=> [3,6,2,7,9,5,4,10,8,1] => [[1,4,7,8,10],[2,5,9],[3],[6]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,1,0,1,0,0,0]
=> [(1,10),(2,3),(4,9),(5,6),(7,8)]
=> [3,6,2,8,9,5,10,7,4,1] => [[1,4,7,9,10],[2,5,8],[3],[6]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,0,1,1,1,0,0,0,0]
=> [(1,10),(2,3),(4,9),(5,8),(6,7)]
=> [3,7,2,8,9,10,6,5,4,1] => [[1,4,8,9,10],[2,5],[3],[6],[7]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,0,0,1,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8),(9,10)]
=> [4,5,6,3,2,1,8,7,10,9] => [[1,5,6,7,9],[2,8,10],[3],[4]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,0,0,1,1,0,0]
=> [(1,6),(2,5),(3,4),(7,10),(8,9)]
=> [4,5,6,3,2,1,9,10,8,7] => [[1,5,6,7,10],[2,8],[3,9],[4]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,0,1,0,0,1,0]
=> [(1,8),(2,5),(3,4),(6,7),(9,10)]
=> [4,5,7,3,2,8,6,1,10,9] => [[1,5,6,8,9],[2,7,10],[3],[4]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,0,1,0,1,0,0]
=> [(1,10),(2,5),(3,4),(6,7),(8,9)]
=> [4,5,7,3,2,9,6,10,8,1] => [[1,5,6,8,10],[2,7,9],[3],[4]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,0,1,1,0,0,0]
=> [(1,10),(2,5),(3,4),(6,9),(7,8)]
=> [4,5,8,3,2,9,10,7,6,1] => [[1,5,6,9,10],[2,7],[3,8],[4]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,1,0,0,0,1,0]
=> [(1,8),(2,7),(3,4),(5,6),(9,10)]
=> [4,6,7,3,8,5,2,1,10,9] => [[1,5,7,8,9],[2,6,10],[3],[4]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,1,0,0,1,0,0]
=> [(1,10),(2,7),(3,4),(5,6),(8,9)]
=> [4,6,7,3,9,5,2,10,8,1] => [[1,5,7,8,10],[2,6,9],[3],[4]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,0,1,0,1,0,0,0]
=> [(1,10),(2,9),(3,4),(5,6),(7,8)]
=> [4,6,8,3,9,5,10,7,2,1] => [[1,5,7,9,10],[2,6,8],[3],[4]]
=> 8
[1,1,1,0,1,1,0,0,0,0]
=> [(1,10),(2,9),(3,4),(5,8),(6,7)]
=> [4,7,8,3,9,10,6,5,2,1] => [[1,5,8,9,10],[2,6],[3],[4],[7]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,1,0,0,0,0,1,0]
=> [(1,8),(2,7),(3,6),(4,5),(9,10)]
=> [5,6,7,8,4,3,2,1,10,9] => [[1,6,7,8,9],[2,10],[3],[4],[5]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,1,0,0,0,1,0,0]
=> [(1,10),(2,7),(3,6),(4,5),(8,9)]
=> [5,6,7,9,4,3,2,10,8,1] => [[1,6,7,8,10],[2,9],[3],[4],[5]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,1,0,0,1,0,0,0]
=> [(1,10),(2,9),(3,6),(4,5),(7,8)]
=> [5,6,8,9,4,3,10,7,2,1] => [[1,6,7,9,10],[2,8],[3],[4],[5]]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11}
[1,1,1,1,0,1,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,5),(6,7)]
=> [5,7,8,9,4,10,6,3,2,1] => [[1,6,8,9,10],[2,7],[3],[4],[5]]
=> 11
[1,1,1,1,1,0,0,0,0,0]
=> [(1,10),(2,9),(3,8),(4,7),(5,6)]
=> [6,7,8,9,10,5,4,3,2,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]]
=> 15
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]
=> [2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]]
=> 6
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)]
=> [2,1,4,3,6,5,8,7,11,12,10,9] => [[1,3,5,7,9,12],[2,4,6,8,10],[11]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)]
=> [2,1,4,3,6,5,9,10,8,7,12,11] => [[1,3,5,7,10,11],[2,4,6,8,12],[9]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)]
=> [2,1,4,3,6,5,9,11,8,12,10,7] => [[1,3,5,7,10,12],[2,4,6,8,11],[9]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)]
=> [2,1,4,3,6,5,10,11,12,9,8,7] => [[1,3,5,7,11,12],[2,4,6,8],[9],[10]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)]
=> [2,1,4,3,7,8,6,5,10,9,12,11] => [[1,3,5,8,9,11],[2,4,6,10,12],[7]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)]
=> [2,1,4,3,7,8,6,5,11,12,10,9] => [[1,3,5,8,9,12],[2,4,6,10],[7,11]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)]
=> [2,1,4,3,7,9,6,10,8,5,12,11] => [[1,3,5,8,10,11],[2,4,6,9,12],[7]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)]
=> [2,1,4,3,7,9,6,11,8,12,10,5] => [[1,3,5,8,10,12],[2,4,6,9,11],[7]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)]
=> [2,1,4,3,7,10,6,11,12,9,8,5] => [[1,3,5,8,11,12],[2,4,6,9],[7],[10]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)]
=> [2,1,4,3,8,9,10,7,6,5,12,11] => [[1,3,5,9,10,11],[2,4,6,12],[7],[8]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)]
=> [2,1,4,3,8,9,11,7,6,12,10,5] => [[1,3,5,9,10,12],[2,4,6,11],[7],[8]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)]
=> [2,1,4,3,8,10,11,7,12,9,6,5] => [[1,3,5,9,11,12],[2,4,6,10],[7],[8]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)]
=> [2,1,4,3,9,10,11,12,8,7,6,5] => [[1,3,5,10,11,12],[2,4,6],[7],[8],[9]]
=> ? ∊ {7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21}
Description
The leg major index of a standard tableau.
The leg length of a cell is the number of cells strictly below in the same column. This statistic is the sum of all leg lengths. Therefore, this is actually a statistic on the underlying integer partition.
It happens to coincide with the (leg) major index of a tabloid restricted to standard Young tableaux, defined as follows: the descent set of a tabloid is the set of cells, not in the top row, whose entry is strictly larger than the entry directly above it. The leg major index is the sum of the leg lengths of the descents plus the number of descents.
Matching statistic: St001003
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
St001003: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 47%
Mp00227: Dyck paths —Delest-Viennot-inverse⟶ Dyck paths
Mp00121: Dyck paths —Cori-Le Borgne involution⟶ Dyck paths
St001003: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 47%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> 4 = 1 + 3
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> 5 = 2 + 3
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> 6 = 3 + 3
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> 6 = 3 + 3
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> 7 = 4 + 3
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 7 = 4 + 3
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> 9 = 6 + 3
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> 7 = 4 + 3
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 7 = 4 + 3
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> 8 = 5 + 3
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> 8 = 5 + 3
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> 10 = 7 + 3
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> 8 = 5 + 3
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> 8 = 5 + 3
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 10 = 7 + 3
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> 10 = 7 + 3
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> 13 = 10 + 3
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> 10 = 7 + 3
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> 8 = 5 + 3
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> 9 = 6 + 3
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> 8 = 5 + 3
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> 10 = 7 + 3
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> ? ∊ {5,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15} + 3
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [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]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=> ? ∊ {6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14,14,14,16,16,16,16,16,16,16,16,16,21} + 3
Description
The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path.
Matching statistic: St001232
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 59%
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
Mp00124: Dyck paths —Adin-Bagno-Roichman transformation⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 59%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,0,1,0]
=> 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> ? = 3
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> 2
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {4,4,6}
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0]
=> ? ∊ {4,4,6}
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> 3
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> ? ∊ {4,4,6}
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,0,0]
=> 4
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> 4
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 5
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> ? ∊ {5,5,5,5,5,7,7,7,7,7,10}
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 6
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> 5
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> 7
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> 6
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0,1,0]
=> 7
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,1,1,0,1,0,0,0,1,1,0,0]
=> ? ∊ {6,6,6,6,6,6,6,6,6,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,10,11,11,11,11,11,11,11,15}
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> 8
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> 6
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=> 8
[1,1,0,0,1,1,1,1,0,0,0,0]
=> [1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> 10
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=> 7
[1,1,1,0,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=> 10
[1,1,1,1,0,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=> 8
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=> 9
[1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=> 10
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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