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Your data matches 7 different statistics following compositions of up to 3 maps.
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Matching statistic: St000419
(load all 8 compositions to match this statistic)
(load all 8 compositions to match this statistic)
St000419: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> 1
[1,1,0,0]
=> 0
[1,0,1,0,1,0]
=> 4
[1,0,1,1,0,0]
=> 2
[1,1,0,0,1,0]
=> 2
[1,1,0,1,0,0]
=> 1
[1,1,1,0,0,0]
=> 0
[1,0,1,0,1,0,1,0]
=> 13
[1,0,1,0,1,1,0,0]
=> 8
[1,0,1,1,0,0,1,0]
=> 9
[1,0,1,1,0,1,0,0]
=> 6
[1,0,1,1,1,0,0,0]
=> 3
[1,1,0,0,1,0,1,0]
=> 8
[1,1,0,0,1,1,0,0]
=> 5
[1,1,0,1,0,0,1,0]
=> 6
[1,1,0,1,0,1,0,0]
=> 4
[1,1,0,1,1,0,0,0]
=> 2
[1,1,1,0,0,0,1,0]
=> 3
[1,1,1,0,0,1,0,0]
=> 2
[1,1,1,0,1,0,0,0]
=> 1
[1,1,1,1,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> 41
[1,0,1,0,1,0,1,1,0,0]
=> 27
[1,0,1,0,1,1,0,0,1,0]
=> 31
[1,0,1,0,1,1,0,1,0,0]
=> 22
[1,0,1,0,1,1,1,0,0,0]
=> 13
[1,0,1,1,0,0,1,0,1,0]
=> 31
[1,0,1,1,0,0,1,1,0,0]
=> 21
[1,0,1,1,0,1,0,0,1,0]
=> 25
[1,0,1,1,0,1,0,1,0,0]
=> 18
[1,0,1,1,0,1,1,0,0,0]
=> 11
[1,0,1,1,1,0,0,0,1,0]
=> 16
[1,0,1,1,1,0,0,1,0,0]
=> 12
[1,0,1,1,1,0,1,0,0,0]
=> 8
[1,0,1,1,1,1,0,0,0,0]
=> 4
[1,1,0,0,1,0,1,0,1,0]
=> 27
[1,1,0,0,1,0,1,1,0,0]
=> 18
[1,1,0,0,1,1,0,0,1,0]
=> 21
[1,1,0,0,1,1,0,1,0,0]
=> 15
[1,1,0,0,1,1,1,0,0,0]
=> 9
[1,1,0,1,0,0,1,0,1,0]
=> 22
[1,1,0,1,0,0,1,1,0,0]
=> 15
[1,1,0,1,0,1,0,0,1,0]
=> 18
[1,1,0,1,0,1,0,1,0,0]
=> 13
[1,1,0,1,0,1,1,0,0,0]
=> 8
[1,1,0,1,1,0,0,0,1,0]
=> 12
[1,1,0,1,1,0,0,1,0,0]
=> 9
[1,1,0,1,1,0,1,0,0,0]
=> 6
[1,1,0,1,1,1,0,0,0,0]
=> 3
[1,1,1,0,0,0,1,0,1,0]
=> 13
Description
The number of Dyck paths that are weakly above the Dyck path, except for the path itself.
Matching statistic: St000420
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
St000420: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
=> 2 = 1 + 1
[1,1,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0]
=> 5 = 4 + 1
[1,0,1,1,0,0]
=> 3 = 2 + 1
[1,1,0,0,1,0]
=> 3 = 2 + 1
[1,1,0,1,0,0]
=> 2 = 1 + 1
[1,1,1,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> 14 = 13 + 1
[1,0,1,0,1,1,0,0]
=> 9 = 8 + 1
[1,0,1,1,0,0,1,0]
=> 10 = 9 + 1
[1,0,1,1,0,1,0,0]
=> 7 = 6 + 1
[1,0,1,1,1,0,0,0]
=> 4 = 3 + 1
[1,1,0,0,1,0,1,0]
=> 9 = 8 + 1
[1,1,0,0,1,1,0,0]
=> 6 = 5 + 1
[1,1,0,1,0,0,1,0]
=> 7 = 6 + 1
[1,1,0,1,0,1,0,0]
=> 5 = 4 + 1
[1,1,0,1,1,0,0,0]
=> 3 = 2 + 1
[1,1,1,0,0,0,1,0]
=> 4 = 3 + 1
[1,1,1,0,0,1,0,0]
=> 3 = 2 + 1
[1,1,1,0,1,0,0,0]
=> 2 = 1 + 1
[1,1,1,1,0,0,0,0]
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> 42 = 41 + 1
[1,0,1,0,1,0,1,1,0,0]
=> 28 = 27 + 1
[1,0,1,0,1,1,0,0,1,0]
=> 32 = 31 + 1
[1,0,1,0,1,1,0,1,0,0]
=> 23 = 22 + 1
[1,0,1,0,1,1,1,0,0,0]
=> 14 = 13 + 1
[1,0,1,1,0,0,1,0,1,0]
=> 32 = 31 + 1
[1,0,1,1,0,0,1,1,0,0]
=> 22 = 21 + 1
[1,0,1,1,0,1,0,0,1,0]
=> 26 = 25 + 1
[1,0,1,1,0,1,0,1,0,0]
=> 19 = 18 + 1
[1,0,1,1,0,1,1,0,0,0]
=> 12 = 11 + 1
[1,0,1,1,1,0,0,0,1,0]
=> 17 = 16 + 1
[1,0,1,1,1,0,0,1,0,0]
=> 13 = 12 + 1
[1,0,1,1,1,0,1,0,0,0]
=> 9 = 8 + 1
[1,0,1,1,1,1,0,0,0,0]
=> 5 = 4 + 1
[1,1,0,0,1,0,1,0,1,0]
=> 28 = 27 + 1
[1,1,0,0,1,0,1,1,0,0]
=> 19 = 18 + 1
[1,1,0,0,1,1,0,0,1,0]
=> 22 = 21 + 1
[1,1,0,0,1,1,0,1,0,0]
=> 16 = 15 + 1
[1,1,0,0,1,1,1,0,0,0]
=> 10 = 9 + 1
[1,1,0,1,0,0,1,0,1,0]
=> 23 = 22 + 1
[1,1,0,1,0,0,1,1,0,0]
=> 16 = 15 + 1
[1,1,0,1,0,1,0,0,1,0]
=> 19 = 18 + 1
[1,1,0,1,0,1,0,1,0,0]
=> 14 = 13 + 1
[1,1,0,1,0,1,1,0,0,0]
=> 9 = 8 + 1
[1,1,0,1,1,0,0,0,1,0]
=> 13 = 12 + 1
[1,1,0,1,1,0,0,1,0,0]
=> 10 = 9 + 1
[1,1,0,1,1,0,1,0,0,0]
=> 7 = 6 + 1
[1,1,0,1,1,1,0,0,0,0]
=> 4 = 3 + 1
[1,1,1,0,0,0,1,0,1,0]
=> 14 = 13 + 1
Description
The number of Dyck paths that are weakly above a Dyck path.
Matching statistic: St001389
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001389: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 44%●distinct values known / distinct values provided: 29%
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001389: Integer partitions ⟶ ℤResult quality: 29% ●values known / values provided: 44%●distinct values known / distinct values provided: 29%
Values
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1]
=> 1 = 0 + 1
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [2,1]
=> 2 = 1 + 1
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> [3,1,1]
=> 3 = 2 + 1
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [2,1,1]
=> 2 = 1 + 1
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,1]
=> 1 = 0 + 1
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 3 = 2 + 1
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 5 = 4 + 1
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> 6 = 5 + 1
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> 3 = 2 + 1
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> 9 = 8 + 1
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> 7 = 6 + 1
[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]
=> [3,2,1,1]
=> 5 = 4 + 1
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> 3 = 2 + 1
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> 1 = 0 + 1
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> 4 = 3 + 1
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> 10 = 9 + 1
[1,1,0,1,1,0,0,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 7 = 6 + 1
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> 2 = 1 + 1
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> 4 = 3 + 1
[1,1,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 9 = 8 + 1
[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]
=> [4,3,2,1]
=> 14 = 13 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> 22 = 21 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> 13 = 12 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> 16 = 15 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [4,2,2,1,1]
=> 10 = 9 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [2,2,2,1,1]
=> 4 = 3 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> 10 = 9 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [3,2,2,1,1]
=> 7 = 6 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> 19 = 18 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> 16 = 15 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [3,3,2,1,1]
=> 9 = 8 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> 28 = 27 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> 23 = 22 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,1]
=> 19 = 18 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> 14 = 13 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> 12 = 11 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [5,1,1,1,1]
=> 5 = 4 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,1,1]
=> 9 = 8 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [4,1,1,1,1]
=> 4 = 3 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [2,1,1,1,1]
=> 2 = 1 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [3,3,1,1,1]
=> 6 = 5 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [3,1,1,1,1]
=> 3 = 2 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> 10 = 9 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> 22 = 21 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> 12 = 11 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,1,1]
=> 14 = 13 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> 32 = 31 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> 26 = 25 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> 19 = 18 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [2,2,1,1,1]
=> 3 = 2 + 1
[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]
=> [1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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]
=> [1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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]
=> [1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,4,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,4,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,5,4,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,5,3,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=> [6,5,4,1,1,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,5,3,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=> [6,5,2,2,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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]
=> [1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,3,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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]
=> [1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,4,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,4,4,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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]
=> [6,5,4,3,2,1]
=> ? ∊ {47,47,52,52,52,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> [7,5,5,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=> [7,5,5,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
=> [7,4,4,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
=> [7,4,4,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [7,4,2,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=> [6,5,5,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
=> [6,5,5,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
=> [6,4,4,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [6,4,4,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=> [6,4,2,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=> [4,4,4,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=> [4,4,4,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=> [5,5,5,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
=> [5,5,5,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=> [5,4,4,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=> [5,4,4,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=> [6,6,5,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
=> [6,6,5,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=> [6,6,4,3,3,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
=> [6,6,4,2,2,1,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
Description
The number of partitions of the same length below the given integer partition.
For a partition $\lambda_1 \geq \dots \lambda_k > 0$, this number is
$$ \det\left( \binom{\lambda_{k+1-i}}{j-i+1} \right)_{1 \le i,j \le k}.$$
Matching statistic: St000108
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000108: Integer partitions ⟶ ℤResult quality: 24% ●values known / values provided: 42%●distinct values known / distinct values provided: 24%
St000108: Integer partitions ⟶ ℤResult quality: 24% ●values known / values provided: 42%●distinct values known / distinct values provided: 24%
Values
[1,0,1,0]
=> [1]
=> 2 = 1 + 1
[1,1,0,0]
=> []
=> 1 = 0 + 1
[1,0,1,0,1,0]
=> [2,1]
=> 5 = 4 + 1
[1,0,1,1,0,0]
=> [1,1]
=> 3 = 2 + 1
[1,1,0,0,1,0]
=> [2]
=> 3 = 2 + 1
[1,1,0,1,0,0]
=> [1]
=> 2 = 1 + 1
[1,1,1,0,0,0]
=> []
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> 14 = 13 + 1
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> 9 = 8 + 1
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> 10 = 9 + 1
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> 7 = 6 + 1
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> 4 = 3 + 1
[1,1,0,0,1,0,1,0]
=> [3,2]
=> 9 = 8 + 1
[1,1,0,0,1,1,0,0]
=> [2,2]
=> 6 = 5 + 1
[1,1,0,1,0,0,1,0]
=> [3,1]
=> 7 = 6 + 1
[1,1,0,1,0,1,0,0]
=> [2,1]
=> 5 = 4 + 1
[1,1,0,1,1,0,0,0]
=> [1,1]
=> 3 = 2 + 1
[1,1,1,0,0,0,1,0]
=> [3]
=> 4 = 3 + 1
[1,1,1,0,0,1,0,0]
=> [2]
=> 3 = 2 + 1
[1,1,1,0,1,0,0,0]
=> [1]
=> 2 = 1 + 1
[1,1,1,1,0,0,0,0]
=> []
=> 1 = 0 + 1
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> 42 = 41 + 1
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> 28 = 27 + 1
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> 32 = 31 + 1
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> 23 = 22 + 1
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> 14 = 13 + 1
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> 32 = 31 + 1
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> 22 = 21 + 1
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> 26 = 25 + 1
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> 19 = 18 + 1
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> 12 = 11 + 1
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> 17 = 16 + 1
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> 13 = 12 + 1
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> 9 = 8 + 1
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> 5 = 4 + 1
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> 28 = 27 + 1
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> 19 = 18 + 1
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> 22 = 21 + 1
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> 16 = 15 + 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> 10 = 9 + 1
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> 23 = 22 + 1
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> 16 = 15 + 1
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> 19 = 18 + 1
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> 14 = 13 + 1
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> 9 = 8 + 1
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> 13 = 12 + 1
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> 10 = 9 + 1
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> 7 = 6 + 1
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> 4 = 3 + 1
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> 14 = 13 + 1
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [3,3,2,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [4,2,2,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [3,3,3,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [5,2,2,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [4,4,1,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [4,4,3,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [5,3,3,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [4,3,3,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [3,3,3,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [5,4,2,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [4,4,2,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [5,3,2,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,0,1,0,1,0,0]
=> [4,3,2,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,1,0,0,0,1,0]
=> [5,2,2,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,0,1,0,1,1,0,0]
=> [4,4,3,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,0,1,1,0,0,1,0]
=> [5,3,3,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,0,1,1,0,1,0,0]
=> [4,3,3,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,1,0,0,1,1,0,0]
=> [4,4,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,1,1,0,0,0,1,0,1,0]
=> [5,4,1,1]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,0,0,1,0,1,0,1,0]
=> [5,4,3]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,0,0,1,0,1,1,0,0]
=> [4,4,3]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,0,0,1,1,0,0,1,0]
=> [5,3,3]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,1,0,0,1,0,0,1,0,1,0]
=> [5,4,2]
=> ? ∊ {33,33,39,39,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,5,4,3,2,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,4,3,2,1]
=> ? ∊ {26,26,33,33,34,34,35,35,36,39,39,42,42,42,42,44,44,45,45,45,45,45,46,46,46,46,47,47,47,47,49,49,49,49,49,49,50,50,50,50,51,51,51,51,52,52,52,53,53,54,54,54,54,54,54,54,54,55,55,60,60,60,60,61,61,61,61,61,61,61,61,62,62,64,64,64,64,65,65,65,65,65,65,66,66,66,66,68,69,69,69,69,70,70,71,71,74,74,74,74,74,74,74,75,75,75,75,77,77,78,78,78,78,79,79,80,80,80,80,81,81,82,82,83,84,84,86,86,88,88,88,88,89,89,90,90,93,93,94,94,94,94,94,94,95,95,95,95,96,96,96,96,98,98,98,98,102,102,103,103,104,104,104,104,105,105,106,106,106,107,107,108,108,109,109,111,111,112,112,113,113,114,114,115,115,116,116,117,117,117,120,120,122,122,122,122,124,124,125,126,126,128,128,131,131,131,133,135,135,135,135,136,136,138,138,139,139,141,141,144,144,144,144,144,144,144,144,145,145,150,150,150,150,155,155,155,156,156,156,156,157,157,160,160,161,162,162,164,164,170,170,170,170,172,172,173,173,178,178,179,179,180,184,184,187,187,188,188,192,192,198,198,201,201,204,204,206,208,208,210,210,213,213,218,218,219,219,224,224,226,226,229,232,240,240,250,250,251,251,254,254,254,254,267,267,280,294,294,296,296,302,302,313,344,344,358,358,428} + 1
Description
The number of partitions contained in the given partition.
Matching statistic: St001313
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00146: Dyck paths —to tunnel matching⟶ Perfect matchings
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
St001313: Binary words ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 14%
Mp00283: Perfect matchings —non-nesting-exceedence permutation⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
St001313: Binary words ⟶ ℤResult quality: 10% ●values known / values provided: 10%●distinct values known / distinct values provided: 14%
Values
[1,0,1,0]
=> [(1,2),(3,4)]
=> [2,1,4,3] => 101 => 2 = 1 + 1
[1,1,0,0]
=> [(1,4),(2,3)]
=> [3,4,2,1] => 110 => 1 = 0 + 1
[1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6)]
=> [2,1,4,3,6,5] => 10101 => 5 = 4 + 1
[1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5)]
=> [2,1,5,6,4,3] => 10110 => 3 = 2 + 1
[1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6)]
=> [3,4,2,1,6,5] => 11001 => 3 = 2 + 1
[1,1,0,1,0,0]
=> [(1,6),(2,3),(4,5)]
=> [3,5,2,6,4,1] => 11010 => 2 = 1 + 1
[1,1,1,0,0,0]
=> [(1,6),(2,5),(3,4)]
=> [4,5,6,3,2,1] => 11100 => 1 = 0 + 1
[1,0,1,0,1,0,1,0]
=> [(1,2),(3,4),(5,6),(7,8)]
=> [2,1,4,3,6,5,8,7] => 1010101 => 14 = 13 + 1
[1,0,1,0,1,1,0,0]
=> [(1,2),(3,4),(5,8),(6,7)]
=> [2,1,4,3,7,8,6,5] => 1010110 => 9 = 8 + 1
[1,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8)]
=> [2,1,5,6,4,3,8,7] => 1011001 => 10 = 9 + 1
[1,0,1,1,0,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7)]
=> [2,1,5,7,4,8,6,3] => 1011010 => 7 = 6 + 1
[1,0,1,1,1,0,0,0]
=> [(1,2),(3,8),(4,7),(5,6)]
=> [2,1,6,7,8,5,4,3] => 1011100 => 4 = 3 + 1
[1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8)]
=> [3,4,2,1,6,5,8,7] => 1100101 => 9 = 8 + 1
[1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7)]
=> [3,4,2,1,7,8,6,5] => 1100110 => 6 = 5 + 1
[1,1,0,1,0,0,1,0]
=> [(1,6),(2,3),(4,5),(7,8)]
=> [3,5,2,6,4,1,8,7] => 1101001 => 7 = 6 + 1
[1,1,0,1,0,1,0,0]
=> [(1,8),(2,3),(4,5),(6,7)]
=> [3,5,2,7,4,8,6,1] => 1101010 => 5 = 4 + 1
[1,1,0,1,1,0,0,0]
=> [(1,8),(2,3),(4,7),(5,6)]
=> [3,6,2,7,8,5,4,1] => 1101100 => 3 = 2 + 1
[1,1,1,0,0,0,1,0]
=> [(1,6),(2,5),(3,4),(7,8)]
=> [4,5,6,3,2,1,8,7] => 1110001 => 4 = 3 + 1
[1,1,1,0,0,1,0,0]
=> [(1,8),(2,5),(3,4),(6,7)]
=> [4,5,7,3,2,8,6,1] => 1110010 => 3 = 2 + 1
[1,1,1,0,1,0,0,0]
=> [(1,8),(2,7),(3,4),(5,6)]
=> [4,6,7,3,8,5,2,1] => 1110100 => 2 = 1 + 1
[1,1,1,1,0,0,0,0]
=> [(1,8),(2,7),(3,6),(4,5)]
=> [5,6,7,8,4,3,2,1] => 1111000 => 1 = 0 + 1
[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] => 101010101 => 42 = 41 + 1
[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] => 101010110 => 28 = 27 + 1
[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] => 101011001 => 32 = 31 + 1
[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] => 101011010 => 23 = 22 + 1
[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] => 101011100 => 14 = 13 + 1
[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] => 101100101 => 32 = 31 + 1
[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] => 101100110 => 22 = 21 + 1
[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] => 101101001 => 26 = 25 + 1
[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] => 101101010 => 19 = 18 + 1
[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] => 101101100 => 12 = 11 + 1
[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] => 101110001 => 17 = 16 + 1
[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] => 101110010 => 13 = 12 + 1
[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] => 101110100 => 9 = 8 + 1
[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] => 101111000 => 5 = 4 + 1
[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] => 110010101 => 28 = 27 + 1
[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] => 110010110 => 19 = 18 + 1
[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] => 110011001 => 22 = 21 + 1
[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] => 110011010 => 16 = 15 + 1
[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] => 110011100 => 10 = 9 + 1
[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] => 110100101 => 23 = 22 + 1
[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] => 110100110 => 16 = 15 + 1
[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] => 110101001 => 19 = 18 + 1
[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] => 110101010 => 14 = 13 + 1
[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] => 110101100 => 9 = 8 + 1
[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] => 110110001 => 13 = 12 + 1
[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] => 110110010 => 10 = 9 + 1
[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] => 110110100 => 7 = 6 + 1
[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] => 110111000 => 4 = 3 + 1
[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] => 111000101 => 14 = 13 + 1
[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] => 10101010101 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101010110 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101011001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101011010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101011100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101100101 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101100110 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101101001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101101010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101101100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101110001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101110010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101110100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[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] => 10101111000 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)]
=> [2,1,5,6,4,3,8,7,10,9,12,11] => 10110010101 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)]
=> [2,1,5,6,4,3,8,7,11,12,10,9] => 10110010110 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)]
=> [2,1,5,6,4,3,9,10,8,7,12,11] => 10110011001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)]
=> [2,1,5,6,4,3,9,11,8,12,10,7] => 10110011010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)]
=> [2,1,5,6,4,3,10,11,12,9,8,7] => 10110011100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)]
=> [2,1,5,7,4,8,6,3,10,9,12,11] => 10110100101 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)]
=> [2,1,5,7,4,8,6,3,11,12,10,9] => 10110100110 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)]
=> [2,1,5,7,4,9,6,10,8,3,12,11] => 10110101001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,1,0,1,0,0]
=> [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)]
=> [2,1,5,7,4,9,6,11,8,12,10,3] => 10110101010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,0,1,1,0,0,0]
=> [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)]
=> [2,1,5,7,4,10,6,11,12,9,8,3] => 10110101100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,1,0,0,0,1,0]
=> [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)]
=> [2,1,5,8,4,9,10,7,6,3,12,11] => 10110110001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,1,0,0,1,0,0]
=> [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)]
=> [2,1,5,8,4,9,11,7,6,12,10,3] => 10110110010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,1,0,1,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)]
=> [2,1,5,8,4,10,11,7,12,9,6,3] => 10110110100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,0,1,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)]
=> [2,1,5,9,4,10,11,12,8,7,6,3] => 10110111000 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,0,1,0,1,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)]
=> [2,1,6,7,8,5,4,3,10,9,12,11] => 10111000101 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,0,1,1,0,0]
=> [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)]
=> [2,1,6,7,8,5,4,3,11,12,10,9] => 10111000110 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,1,0,0,1,0]
=> [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)]
=> [2,1,6,7,9,5,4,10,8,3,12,11] => 10111001001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,1,0,1,0,0]
=> [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)]
=> [2,1,6,7,9,5,4,11,8,12,10,3] => 10111001010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,0,1,1,0,0,0]
=> [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)]
=> [2,1,6,7,10,5,4,11,12,9,8,3] => 10111001100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,1,0,0,0,1,0]
=> [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)]
=> [2,1,6,8,9,5,10,7,4,3,12,11] => 10111010001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,1,0,0,1,0,0]
=> [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)]
=> [2,1,6,8,9,5,11,7,4,12,10,3] => 10111010010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,1,0,1,0,0,0]
=> [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)]
=> [2,1,6,8,10,5,11,7,12,9,4,3] => 10111010100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,0,1,1,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)]
=> [2,1,6,9,10,5,11,12,8,7,4,3] => 10111011000 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,0,0,0,0,1,0]
=> [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)]
=> [2,1,7,8,9,10,6,5,4,3,12,11] => 10111100001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,0,0,0,1,0,0]
=> [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)]
=> [2,1,7,8,9,11,6,5,4,12,10,3] => 10111100010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,0,0,1,0,0,0]
=> [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)]
=> [2,1,7,8,10,11,6,5,12,9,4,3] => 10111100100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,0,1,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)]
=> [2,1,7,9,10,11,6,12,8,5,4,3] => 10111101000 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)]
=> [2,1,8,9,10,11,12,7,6,5,4,3] => 10111110000 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)]
=> [3,4,2,1,6,5,8,7,10,9,12,11] => 11001010101 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,0,1,1,0,0]
=> [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)]
=> [3,4,2,1,6,5,8,7,11,12,10,9] => 11001010110 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,1,0,0,1,0]
=> [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)]
=> [3,4,2,1,6,5,9,10,8,7,12,11] => 11001011001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,1,0,1,0,0]
=> [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)]
=> [3,4,2,1,6,5,9,11,8,12,10,7] => 11001011010 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,0,1,1,1,0,0,0]
=> [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)]
=> [3,4,2,1,6,5,10,11,12,9,8,7] => 11001011100 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,0,0,1,0,1,0]
=> [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)]
=> [3,4,2,1,7,8,6,5,10,9,12,11] => 11001100101 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,0,0,1,1,0,0]
=> [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)]
=> [3,4,2,1,7,8,6,5,11,12,10,9] => 11001100110 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
[1,1,0,0,1,1,0,1,0,0,1,0]
=> [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)]
=> [3,4,2,1,7,9,6,10,8,5,12,11] => 11001101001 => ? ∊ {0,1,2,2,3,3,4,4,4,5,5,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131} + 1
Description
The number of Dyck paths above the lattice path given by a binary word.
One may treat a binary word as a lattice path starting at the origin and treating $1$'s as steps $(1,0)$ and $0$'s as steps $(0,1)$. Given a binary word $w$, this statistic counts the number of lattice paths from the origin to the same endpoint as $w$ that stay weakly above $w$.
See [[St001312]] for this statistic on compositions treated as bounce paths.
Matching statistic: St001232
(load all 6 compositions to match this statistic)
(load all 6 compositions to match this statistic)
Mp00099: Dyck paths —bounce path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 7%●distinct values known / distinct values provided: 5%
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 5% ●values known / values provided: 7%●distinct values known / distinct values provided: 5%
Values
[1,0,1,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> 0
[1,1,0,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> 1
[1,0,1,0,1,0]
=> [1,0,1,0,1,0]
=> [1,1,1,0,0,0]
=> 0
[1,0,1,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> [1,1,0,0,1,0]
=> 1
[1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 2
[1,1,1,0,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> ? = 4
[1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0]
=> 0
[1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[1,0,1,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> 3
[1,0,1,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> 1
[1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[1,1,0,1,0,0,1,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[1,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[1,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[1,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[1,1,1,1,0,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,9,13}
[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]
=> 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 4
[1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> 3
[1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,1,0,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
[1,1,0,1,0,0,1,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,0,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,1,0,0,0,1,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[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]
=> 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]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> 5
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131}
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131}
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> 4
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131}
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131}
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131}
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131}
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> ? ∊ {4,5,6,6,8,8,8,8,9,9,9,10,10,11,11,12,12,13,13,13,14,14,14,14,15,15,15,15,16,17,17,18,18,18,19,19,19,20,20,21,21,22,22,23,23,24,24,25,25,27,27,27,27,29,29,29,29,30,30,31,31,32,32,33,33,33,33,34,34,36,36,39,39,40,40,41,41,41,41,42,42,44,44,45,46,46,47,47,47,47,52,52,52,53,53,55,55,61,61,61,61,61,62,62,65,65,71,71,74,74,74,75,75,83,88,88,89,89,103,103,106,131}
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> 3
[1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> 1
[1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=> 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=> 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=> 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> 4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001880
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 5%●distinct values known / distinct values provided: 3%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 3% ●values known / values provided: 5%●distinct values known / distinct values provided: 3%
Values
[1,0,1,0]
=> [1]
=> [[1],[]]
=> ([],1)
=> ? ∊ {0,1}
[1,1,0,0]
=> []
=> [[],[]]
=> ([],0)
=> ? ∊ {0,1}
[1,0,1,0,1,0]
=> [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? ∊ {0,1,2,2,4}
[1,0,1,1,0,0]
=> [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? ∊ {0,1,2,2,4}
[1,1,0,0,1,0]
=> [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? ∊ {0,1,2,2,4}
[1,1,0,1,0,0]
=> [1]
=> [[1],[]]
=> ([],1)
=> ? ∊ {0,1,2,2,4}
[1,1,1,0,0,0]
=> []
=> [[],[]]
=> ([],0)
=> ? ∊ {0,1,2,2,4}
[1,0,1,0,1,0,1,0]
=> [3,2,1]
=> [[3,2,1],[]]
=> ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,0,1,0,1,1,0,0]
=> [2,2,1]
=> [[2,2,1],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,0,1,1,0,0,1,0]
=> [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,0,1,1,0,1,0,0]
=> [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,0,1,1,1,0,0,0]
=> [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,0,0,1,0,1,0]
=> [3,2]
=> [[3,2],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,1,0,0,1,1,0,0]
=> [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,0,1,0,0,1,0]
=> [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,1,0,1,0,1,0,0]
=> [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,1,0,1,1,0,0,0]
=> [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,1,1,0,0,0,1,0]
=> [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,1,0,0]
=> [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,1,1,0,1,0,0,0]
=> [1]
=> [[1],[]]
=> ([],1)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,1,1,1,0,0,0,0]
=> []
=> [[],[]]
=> ([],0)
=> ? ∊ {0,1,2,2,5,6,6,8,8,9,13}
[1,0,1,0,1,0,1,0,1,0]
=> [4,3,2,1]
=> [[4,3,2,1],[]]
=> ([(0,5),(0,6),(3,2),(3,8),(4,1),(4,9),(5,3),(5,7),(6,4),(6,7),(7,8),(7,9)],10)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,0,1,0,1,1,0,0]
=> [3,3,2,1]
=> [[3,3,2,1],[]]
=> ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,0,1,1,0,0,1,0]
=> [4,2,2,1]
=> [[4,2,2,1],[]]
=> ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,0,1,1,0,1,0,0]
=> [3,2,2,1]
=> [[3,2,2,1],[]]
=> ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,0,1,1,1,0,0,0]
=> [2,2,2,1]
=> [[2,2,2,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,0,1,0,1,0]
=> [4,3,1,1]
=> [[4,3,1,1],[]]
=> ([(0,5),(0,6),(3,1),(4,2),(4,8),(5,3),(5,7),(6,4),(6,7),(7,8)],9)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,0,1,1,0,0]
=> [3,3,1,1]
=> [[3,3,1,1],[]]
=> ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,1,0,0,1,0]
=> [4,2,1,1]
=> [[4,2,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(5,7),(6,4),(6,7)],8)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,1,0,1,0,0]
=> [3,2,1,1]
=> [[3,2,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,0,1,1,0,0,0]
=> [2,2,1,1]
=> [[2,2,1,1],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,0,0,0,1,0]
=> [4,1,1,1]
=> [[4,1,1,1],[]]
=> ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,0,0,1,0,0]
=> [3,1,1,1]
=> [[3,1,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,0,1,0,0,0]
=> [2,1,1,1]
=> [[2,1,1,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,0,1,1,1,1,0,0,0,0]
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,0,0,1,0,1,0,1,0]
=> [4,3,2]
=> [[4,3,2],[]]
=> ([(0,4),(0,5),(2,7),(3,1),(3,8),(4,2),(4,6),(5,3),(5,6),(6,7),(6,8)],9)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,0,1,1,0,0]
=> [3,3,2]
=> [[3,3,2],[]]
=> ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7)],8)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,1,0,0,1,0]
=> [4,2,2]
=> [[4,2,2],[]]
=> ([(0,4),(0,5),(1,7),(3,2),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,1,0,1,0,0]
=> [3,2,2]
=> [[3,2,2],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,0,1,1,1,0,0,0]
=> [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,0,1,0,0,1,0,1,0]
=> [4,3,1]
=> [[4,3,1],[]]
=> ([(0,4),(0,5),(3,2),(3,7),(4,3),(4,6),(5,1),(5,6),(6,7)],8)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,0,1,1,0,0]
=> [3,3,1]
=> [[3,3,1],[]]
=> ([(0,3),(0,4),(2,6),(3,1),(3,5),(4,2),(4,5),(5,6)],7)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,1,0,0,1,0]
=> [4,2,1]
=> [[4,2,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(4,6),(5,1),(5,6)],7)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,1,0,1,0,0]
=> [3,2,1]
=> [[3,2,1],[]]
=> ([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,0,1,1,0,0,0]
=> [2,2,1]
=> [[2,2,1],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,0,0,0,1,0]
=> [4,1,1]
=> [[4,1,1],[]]
=> ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,0,0,1,0,0]
=> [3,1,1]
=> [[3,1,1],[]]
=> ([(0,3),(0,4),(3,2),(4,1)],5)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,0,1,0,0,0]
=> [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,0,1,1,1,0,0,0,0]
=> [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,0,0,0,1,0,1,0]
=> [4,3]
=> [[4,3],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,0,1,1,0,0]
=> [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,1,0,0,1,0,0,1,0]
=> [4,2]
=> [[4,2],[]]
=> ([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,1,0,1,0,0]
=> [3,2]
=> [[3,2],[]]
=> ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,0,1,1,0,0,0]
=> [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,1,0,1,0,0,0,1,0]
=> [4,1]
=> [[4,1],[]]
=> ([(0,2),(0,4),(3,1),(4,3)],5)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,1,0,0,1,0,0]
=> [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,1,0,1,0,0,0]
=> [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,0,1,1,0,0,0,0]
=> [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? ∊ {0,1,2,2,5,8,8,8,8,9,9,9,11,11,12,12,13,13,13,15,15,16,18,18,18,21,21,22,22,25,27,27,31,31,41}
[1,1,1,1,0,0,0,0,1,0]
=> [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,1,0,0,0,1,0,0]
=> [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,0,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,0,0,1,1,1,0,0,0,0]
=> [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,1,0,1,1,1,0,0,0,0,0]
=> [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,1,0,0,0,1,1,0,0,0]
=> [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,1,1,1,0,0,0,0,0,1,0]
=> [5]
=> [[5],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,1,1,1,0,0,0,0,1,0,0]
=> [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,1,1,0,0,0,1,0,0,0]
=> [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1,1]
=> [[1,1,1,1,1,1],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1,1]
=> [[1,1,1,1,1],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=> [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=> [2,2,2]
=> [[2,2,2],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=> [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=> [3,3]
=> [[3,3],[]]
=> ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=> [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=> [6]
=> [[6],[]]
=> ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> [5]
=> [[5],[]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 5
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=> [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 4
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=> [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 3
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
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