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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St000213
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Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
St000213: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
St000213: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => [1] => 1
[1,0,1,0]
=> [2,1] => [2,1] => 1
[1,1,0,0]
=> [1,2] => [1,2] => 2
[1,0,1,0,1,0]
=> [3,2,1] => [3,2,1] => 2
[1,0,1,1,0,0]
=> [2,3,1] => [3,1,2] => 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => 2
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => 2
[1,1,1,0,0,0]
=> [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => 2
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,1,2] => 2
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [4,1,3,2] => 2
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [4,2,1,3] => 2
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [4,1,2,3] => 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,4,3,2] => 3
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [1,4,2,3] => 2
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [3,1,4,2] => 2
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [3,2,1,4] => 3
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,1,2,4] => 2
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,2,4,3] => 3
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => 3
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => 3
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,1,2] => 3
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [5,4,1,3,2] => 2
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [5,4,2,1,3] => 2
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [5,4,1,2,3] => 2
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [5,1,4,3,2] => 2
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,1,4,2,3] => 2
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [5,3,1,4,2] => 3
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [5,3,2,1,4] => 2
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [5,3,1,2,4] => 2
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [5,1,2,4,3] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,1,3,2,4] => 2
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [5,2,1,3,4] => 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,5,4,3,2] => 3
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [1,5,4,2,3] => 3
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [1,5,2,4,3] => 3
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [1,5,3,2,4] => 3
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [1,5,2,3,4] => 2
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,1,5,3,2] => 2
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [4,1,5,2,3] => 2
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [4,3,1,5,2] => 3
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => 3
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,1,2,5] => 3
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [4,1,2,5,3] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [4,1,3,2,5] => 3
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [4,2,1,3,5] => 3
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => 2
Description
The number of weak exceedances (also weak excedences) of a permutation.
This is defined as
$$\operatorname{wex}(\sigma)=\#\{i:\sigma(i) \geq i\}.$$
The number of weak exceedances is given by the number of exceedances (see [[St000155]]) plus the number of fixed points (see [[St000022]]) of $\sigma$.
Matching statistic: St000245
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
St000245: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
St000245: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => [1] => [1] => 0 = 1 - 1
[1,0,1,0]
=> [2,1] => [2,1] => [2,1] => 0 = 1 - 1
[1,1,0,0]
=> [1,2] => [1,2] => [1,2] => 1 = 2 - 1
[1,0,1,0,1,0]
=> [3,2,1] => [3,2,1] => [2,3,1] => 1 = 2 - 1
[1,0,1,1,0,0]
=> [2,3,1] => [3,1,2] => [3,2,1] => 0 = 1 - 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => [1,3,2] => 1 = 2 - 1
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => [2,1,3] => 1 = 2 - 1
[1,1,1,0,0,0]
=> [1,2,3] => [1,2,3] => [1,2,3] => 2 = 3 - 1
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => [3,2,4,1] => 1 = 2 - 1
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,1,2] => [4,2,3,1] => 1 = 2 - 1
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [4,1,3,2] => [3,4,2,1] => 1 = 2 - 1
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [4,2,1,3] => [2,4,3,1] => 1 = 2 - 1
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [4,1,2,3] => [4,3,2,1] => 0 = 1 - 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,4,3,2] => [1,3,4,2] => 2 = 3 - 1
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [1,4,2,3] => [1,4,3,2] => 1 = 2 - 1
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [3,1,4,2] => [4,2,1,3] => 1 = 2 - 1
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [3,2,1,4] => [2,3,1,4] => 2 = 3 - 1
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,1,2,4] => [3,2,1,4] => 1 = 2 - 1
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,2,4,3] => [1,2,4,3] => 2 = 3 - 1
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => [1,3,2,4] => 2 = 3 - 1
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2 = 3 - 1
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 3 = 4 - 1
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [3,4,2,5,1] => 2 = 3 - 1
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,1,2] => [3,5,2,4,1] => 2 = 3 - 1
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [5,4,1,3,2] => [5,2,4,3,1] => 1 = 2 - 1
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [5,4,2,1,3] => [5,3,2,4,1] => 1 = 2 - 1
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [5,4,1,2,3] => [4,2,5,3,1] => 1 = 2 - 1
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [5,1,4,3,2] => [4,3,5,2,1] => 1 = 2 - 1
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,1,4,2,3] => [5,3,4,2,1] => 1 = 2 - 1
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [5,3,1,4,2] => [4,5,2,3,1] => 2 = 3 - 1
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [5,3,2,1,4] => [3,2,5,4,1] => 1 = 2 - 1
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [5,3,1,2,4] => [5,4,2,3,1] => 1 = 2 - 1
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [5,1,2,4,3] => [4,5,3,2,1] => 1 = 2 - 1
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,1,3,2,4] => [3,5,4,2,1] => 1 = 2 - 1
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [5,2,1,3,4] => [2,5,4,3,1] => 1 = 2 - 1
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [5,4,3,2,1] => 0 = 1 - 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,5,4,3,2] => [1,4,3,5,2] => 2 = 3 - 1
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [1,5,4,2,3] => [1,5,3,4,2] => 2 = 3 - 1
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [1,5,2,4,3] => [1,4,5,3,2] => 2 = 3 - 1
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [1,5,3,2,4] => [1,3,5,4,2] => 2 = 3 - 1
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [1,5,2,3,4] => [1,5,4,3,2] => 1 = 2 - 1
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,1,5,3,2] => [5,2,1,4,3] => 1 = 2 - 1
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [4,1,5,2,3] => [4,2,1,5,3] => 1 = 2 - 1
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [4,3,1,5,2] => [5,2,3,1,4] => 2 = 3 - 1
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [3,2,4,1,5] => 2 = 3 - 1
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,1,2,5] => [4,2,3,1,5] => 2 = 3 - 1
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [4,1,2,5,3] => [5,3,2,1,4] => 1 = 2 - 1
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [4,1,3,2,5] => [3,4,2,1,5] => 2 = 3 - 1
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [4,2,1,3,5] => [2,4,3,1,5] => 2 = 3 - 1
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [4,3,2,1,5] => 1 = 2 - 1
Description
The number of ascents of a permutation.
Matching statistic: St000702
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000702: Permutations ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000702: Permutations ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => [1] => [1] => ? = 1
[1,0,1,0]
=> [2,1] => [2,1] => [2,1] => 1
[1,1,0,0]
=> [1,2] => [1,2] => [1,2] => 2
[1,0,1,0,1,0]
=> [3,2,1] => [3,2,1] => [3,2,1] => 2
[1,0,1,1,0,0]
=> [2,3,1] => [3,1,2] => [2,3,1] => 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => [1,3,2] => 2
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,1,1,0,0,0]
=> [1,2,3] => [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 2
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,1,2] => [3,4,2,1] => 2
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [4,1,3,2] => [2,4,3,1] => 2
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [4,2,1,3] => [3,2,4,1] => 2
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [4,1,2,3] => [2,3,4,1] => 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 3
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [1,4,2,3] => [1,3,4,2] => 2
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [3,1,4,2] => [2,4,1,3] => 2
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,1,2,4] => [2,3,1,4] => 2
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,2,4,3] => [1,2,4,3] => 3
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => [1,3,2,4] => 3
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => 3
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,1,2] => [4,5,3,2,1] => 3
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [5,4,1,3,2] => [3,5,4,2,1] => 2
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [5,4,2,1,3] => [4,3,5,2,1] => 2
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [5,4,1,2,3] => [3,4,5,2,1] => 2
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [5,1,4,3,2] => [2,5,4,3,1] => 2
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,1,4,2,3] => [2,4,5,3,1] => 2
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [5,3,1,4,2] => [3,5,2,4,1] => 3
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [5,3,2,1,4] => [4,3,2,5,1] => 2
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [5,3,1,2,4] => [3,4,2,5,1] => 2
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [5,1,2,4,3] => [2,3,5,4,1] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,1,3,2,4] => [2,4,3,5,1] => 2
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [5,2,1,3,4] => [3,2,4,5,1] => 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [2,3,4,5,1] => 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [1,5,4,2,3] => [1,4,5,3,2] => 3
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [1,5,2,4,3] => [1,3,5,4,2] => 3
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [1,5,3,2,4] => [1,4,3,5,2] => 3
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [1,5,2,3,4] => [1,3,4,5,2] => 2
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,1,5,3,2] => [2,5,4,1,3] => 2
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [4,1,5,2,3] => [2,4,5,1,3] => 2
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [4,3,1,5,2] => [3,5,2,1,4] => 3
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => 3
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,1,2,5] => [3,4,2,1,5] => 3
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [4,1,2,5,3] => [2,3,5,1,4] => 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [4,1,3,2,5] => [2,4,3,1,5] => 3
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [4,2,1,3,5] => [3,2,4,1,5] => 3
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [2,3,4,1,5] => 2
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [1,2,5,4,3] => [1,2,5,4,3] => 4
Description
The number of weak deficiencies of a permutation.
This is defined as
$$\operatorname{wdec}(\sigma)=\#\{i:\sigma(i) \leq i\}.$$
The number of weak exceedances is [[St000213]], the number of deficiencies is [[St000703]].
Matching statistic: St001863
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001863: Signed permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 83%
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001863: Signed permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 83%
Values
[1,0]
=> [1] => [1] => [1] => 1
[1,0,1,0]
=> [2,1] => [2,1] => [2,1] => 1
[1,1,0,0]
=> [1,2] => [1,2] => [1,2] => 2
[1,0,1,0,1,0]
=> [3,2,1] => [3,2,1] => [3,2,1] => 2
[1,0,1,1,0,0]
=> [2,3,1] => [3,1,2] => [3,1,2] => 1
[1,1,0,0,1,0]
=> [3,1,2] => [1,3,2] => [1,3,2] => 2
[1,1,0,1,0,0]
=> [2,1,3] => [2,1,3] => [2,1,3] => 2
[1,1,1,0,0,0]
=> [1,2,3] => [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0]
=> [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 2
[1,0,1,0,1,1,0,0]
=> [3,4,2,1] => [4,3,1,2] => [4,3,1,2] => 2
[1,0,1,1,0,0,1,0]
=> [4,2,3,1] => [4,1,3,2] => [4,1,3,2] => 2
[1,0,1,1,0,1,0,0]
=> [3,2,4,1] => [4,2,1,3] => [4,2,1,3] => 2
[1,0,1,1,1,0,0,0]
=> [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 1
[1,1,0,0,1,0,1,0]
=> [4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 3
[1,1,0,0,1,1,0,0]
=> [3,4,1,2] => [1,4,2,3] => [1,4,2,3] => 2
[1,1,0,1,0,0,1,0]
=> [4,2,1,3] => [3,1,4,2] => [3,1,4,2] => 2
[1,1,0,1,0,1,0,0]
=> [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 3
[1,1,0,1,1,0,0,0]
=> [2,3,1,4] => [3,1,2,4] => [3,1,2,4] => 2
[1,1,1,0,0,0,1,0]
=> [4,1,2,3] => [1,2,4,3] => [1,2,4,3] => 3
[1,1,1,0,0,1,0,0]
=> [3,1,2,4] => [1,3,2,4] => [1,3,2,4] => 3
[1,1,1,0,1,0,0,0]
=> [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,1,1,0,0,0,0]
=> [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0]
=> [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 3
[1,0,1,0,1,0,1,1,0,0]
=> [4,5,3,2,1] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 3
[1,0,1,0,1,1,0,0,1,0]
=> [5,3,4,2,1] => [5,4,1,3,2] => [5,4,1,3,2] => ? = 2
[1,0,1,0,1,1,0,1,0,0]
=> [4,3,5,2,1] => [5,4,2,1,3] => [5,4,2,1,3] => ? = 2
[1,0,1,0,1,1,1,0,0,0]
=> [3,4,5,2,1] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 2
[1,0,1,1,0,0,1,0,1,0]
=> [5,4,2,3,1] => [5,1,4,3,2] => [5,1,4,3,2] => ? = 2
[1,0,1,1,0,0,1,1,0,0]
=> [4,5,2,3,1] => [5,1,4,2,3] => [5,1,4,2,3] => ? = 2
[1,0,1,1,0,1,0,0,1,0]
=> [5,3,2,4,1] => [5,3,1,4,2] => [5,3,1,4,2] => ? = 3
[1,0,1,1,0,1,0,1,0,0]
=> [4,3,2,5,1] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 2
[1,0,1,1,0,1,1,0,0,0]
=> [3,4,2,5,1] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 2
[1,0,1,1,1,0,0,0,1,0]
=> [5,2,3,4,1] => [5,1,2,4,3] => [5,1,2,4,3] => ? = 2
[1,0,1,1,1,0,0,1,0,0]
=> [4,2,3,5,1] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 2
[1,0,1,1,1,0,1,0,0,0]
=> [3,2,4,5,1] => [5,2,1,3,4] => [5,2,1,3,4] => ? = 2
[1,0,1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => [5,1,2,3,4] => [5,1,2,3,4] => ? = 1
[1,1,0,0,1,0,1,0,1,0]
=> [5,4,3,1,2] => [1,5,4,3,2] => [1,5,4,3,2] => 3
[1,1,0,0,1,0,1,1,0,0]
=> [4,5,3,1,2] => [1,5,4,2,3] => [1,5,4,2,3] => 3
[1,1,0,0,1,1,0,0,1,0]
=> [5,3,4,1,2] => [1,5,2,4,3] => [1,5,2,4,3] => 3
[1,1,0,0,1,1,0,1,0,0]
=> [4,3,5,1,2] => [1,5,3,2,4] => [1,5,3,2,4] => 3
[1,1,0,0,1,1,1,0,0,0]
=> [3,4,5,1,2] => [1,5,2,3,4] => [1,5,2,3,4] => 2
[1,1,0,1,0,0,1,0,1,0]
=> [5,4,2,1,3] => [4,1,5,3,2] => [4,1,5,3,2] => ? = 2
[1,1,0,1,0,0,1,1,0,0]
=> [4,5,2,1,3] => [4,1,5,2,3] => [4,1,5,2,3] => ? = 2
[1,1,0,1,0,1,0,0,1,0]
=> [5,3,2,1,4] => [4,3,1,5,2] => [4,3,1,5,2] => ? = 3
[1,1,0,1,0,1,0,1,0,0]
=> [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ? = 3
[1,1,0,1,0,1,1,0,0,0]
=> [3,4,2,1,5] => [4,3,1,2,5] => [4,3,1,2,5] => ? = 3
[1,1,0,1,1,0,0,0,1,0]
=> [5,2,3,1,4] => [4,1,2,5,3] => [4,1,2,5,3] => ? = 2
[1,1,0,1,1,0,0,1,0,0]
=> [4,2,3,1,5] => [4,1,3,2,5] => [4,1,3,2,5] => ? = 3
[1,1,0,1,1,0,1,0,0,0]
=> [3,2,4,1,5] => [4,2,1,3,5] => [4,2,1,3,5] => ? = 3
[1,1,0,1,1,1,0,0,0,0]
=> [2,3,4,1,5] => [4,1,2,3,5] => [4,1,2,3,5] => ? = 2
[1,1,1,0,0,0,1,0,1,0]
=> [5,4,1,2,3] => [1,2,5,4,3] => [1,2,5,4,3] => 4
[1,1,1,0,0,0,1,1,0,0]
=> [4,5,1,2,3] => [1,2,5,3,4] => [1,2,5,3,4] => 3
[1,1,1,0,0,1,0,0,1,0]
=> [5,3,1,2,4] => [1,4,2,5,3] => [1,4,2,5,3] => 3
[1,1,1,0,0,1,0,1,0,0]
=> [4,3,1,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 4
[1,1,1,0,0,1,1,0,0,0]
=> [3,4,1,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => 3
[1,1,1,0,1,0,0,0,1,0]
=> [5,2,1,3,4] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 2
[1,1,1,0,1,0,0,1,0,0]
=> [4,2,1,3,5] => [3,1,4,2,5] => [3,1,4,2,5] => ? = 3
[1,1,1,0,1,0,1,0,0,0]
=> [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 4
[1,1,1,0,1,1,0,0,0,0]
=> [2,3,1,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => ? = 3
[1,1,1,1,0,0,0,0,1,0]
=> [5,1,2,3,4] => [1,2,3,5,4] => [1,2,3,5,4] => 4
[1,1,1,1,0,0,0,1,0,0]
=> [4,1,2,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 4
[1,1,1,1,0,0,1,0,0,0]
=> [3,1,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 4
[1,1,1,1,0,1,0,0,0,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 4
[1,1,1,1,1,0,0,0,0,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 5
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [6,5,4,3,2,1] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ? = 3
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [5,6,4,3,2,1] => [6,5,4,3,1,2] => [6,5,4,3,1,2] => ? = 3
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [6,4,5,3,2,1] => [6,5,4,1,3,2] => [6,5,4,1,3,2] => ? = 3
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [5,4,6,3,2,1] => [6,5,4,2,1,3] => [6,5,4,2,1,3] => ? = 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [4,5,6,3,2,1] => [6,5,4,1,2,3] => [6,5,4,1,2,3] => ? = 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [6,5,3,4,2,1] => [6,5,1,4,3,2] => [6,5,1,4,3,2] => ? = 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [5,6,3,4,2,1] => [6,5,1,4,2,3] => [6,5,1,4,2,3] => ? = 3
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [6,4,3,5,2,1] => [6,5,3,1,4,2] => [6,5,3,1,4,2] => ? = 3
[1,0,1,0,1,1,0,1,0,1,0,0]
=> [5,4,3,6,2,1] => [6,5,3,2,1,4] => [6,5,3,2,1,4] => ? = 3
[1,0,1,0,1,1,0,1,1,0,0,0]
=> [4,5,3,6,2,1] => [6,5,3,1,2,4] => [6,5,3,1,2,4] => ? = 3
[1,0,1,0,1,1,1,0,0,0,1,0]
=> [6,3,4,5,2,1] => [6,5,1,2,4,3] => [6,5,1,2,4,3] => ? = 2
[1,0,1,0,1,1,1,0,0,1,0,0]
=> [5,3,4,6,2,1] => [6,5,1,3,2,4] => [6,5,1,3,2,4] => ? = 2
[1,0,1,0,1,1,1,0,1,0,0,0]
=> [4,3,5,6,2,1] => [6,5,2,1,3,4] => [6,5,2,1,3,4] => ? = 2
[1,0,1,0,1,1,1,1,0,0,0,0]
=> [3,4,5,6,2,1] => [6,5,1,2,3,4] => [6,5,1,2,3,4] => ? = 2
[1,0,1,1,0,0,1,0,1,0,1,0]
=> [6,5,4,2,3,1] => [6,1,5,4,3,2] => [6,1,5,4,3,2] => ? = 3
[1,0,1,1,0,0,1,0,1,1,0,0]
=> [5,6,4,2,3,1] => [6,1,5,4,2,3] => [6,1,5,4,2,3] => ? = 3
[1,0,1,1,0,0,1,1,0,0,1,0]
=> [6,4,5,2,3,1] => [6,1,5,2,4,3] => [6,1,5,2,4,3] => ? = 2
[1,0,1,1,0,0,1,1,0,1,0,0]
=> [5,4,6,2,3,1] => [6,1,5,3,2,4] => [6,1,5,3,2,4] => ? = 2
[1,0,1,1,0,0,1,1,1,0,0,0]
=> [4,5,6,2,3,1] => [6,1,5,2,3,4] => [6,1,5,2,3,4] => ? = 2
[1,0,1,1,0,1,0,0,1,0,1,0]
=> [6,5,3,2,4,1] => [6,4,1,5,3,2] => [6,4,1,5,3,2] => ? = 3
[1,0,1,1,0,1,0,0,1,1,0,0]
=> [5,6,3,2,4,1] => [6,4,1,5,2,3] => [6,4,1,5,2,3] => ? = 3
[1,0,1,1,0,1,0,1,0,0,1,0]
=> [6,4,3,2,5,1] => [6,4,3,1,5,2] => [6,4,3,1,5,2] => ? = 4
Description
The number of weak excedances of a signed permutation.
For a signed permutation $\pi\in\mathfrak H_n$, this is $\lvert\{i\in[n] \mid \pi(i) \geq i\}\rvert$.
Matching statistic: St001553
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00228: Dyck paths —reflect parallelogram polyomino⟶ Dyck paths
St001553: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 67%
Mp00101: Dyck paths —decomposition reverse⟶ Dyck paths
Mp00228: Dyck paths —reflect parallelogram polyomino⟶ Dyck paths
St001553: Dyck paths ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 67%
Values
[1,0]
=> [1,1,0,0]
=> [1,0,1,0]
=> [1,1,0,0]
=> 1
[1,0,1,0]
=> [1,1,0,1,0,0]
=> [1,0,1,1,0,0]
=> [1,1,0,0,1,0]
=> 1
[1,1,0,0]
=> [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,0,0,0]
=> 2
[1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0]
=> 1
[1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 2
[1,1,0,1,0,0]
=> [1,1,1,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,0,1,0]
=> 2
[1,1,1,0,0,0]
=> [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,0]
=> 3
[1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> 2
[1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 2
[1,0,1,1,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 2
[1,0,1,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 2
[1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 1
[1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,0,0,1,0,0]
=> 3
[1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,1,0,0]
=> 2
[1,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 2
[1,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,0,0,0]
=> 3
[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]
=> [1,1,0,1,0,0,1,0,1,0]
=> 2
[1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> 3
[1,1,1,0,0,1,0,0]
=> [1,1,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,0,1,1,0,0]
=> 3
[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]
=> [1,1,0,1,0,1,0,0,1,0]
=> 3
[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]
=> [1,1,0,1,0,1,0,1,0,0]
=> 4
[1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> ? = 3
[1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> ? = 3
[1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> ? = 2
[1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,0,1,1,0,0,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> ? = 2
[1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> ? = 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0,1,0]
=> ? = 2
[1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,0,0,1,0]
=> ? = 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,1,0,0,0]
=> [1,1,0,1,1,0,0,1,1,0,0,0]
=> ? = 3
[1,0,1,1,0,1,0,1,0,0]
=> [1,1,0,1,1,0,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,1,0,0,0,0]
=> [1,1,0,0,1,1,1,0,1,0,0,0]
=> ? = 2
[1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,0,0]
=> [1,0,1,1,0,1,1,0,1,0,0,0]
=> [1,1,0,0,1,1,1,1,0,0,0,0]
=> ? = 2
[1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0,1,0]
=> ? = 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,1,1,0,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,1,0,0]
=> [1,1,0,0,1,1,1,0,0,0,1,0]
=> ? = 2
[1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,1,1,0,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,1,0,0,0]
=> [1,1,0,0,1,0,1,1,1,0,0,0]
=> ? = 2
[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]
=> [1,1,0,0,1,0,1,0,1,0,1,0]
=> ? = 1
[1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,0,0,0,0,1,0]
=> [1,1,0,1,1,0,1,0,0,1,0,0]
=> ? = 3
[1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,0,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,0,1,0,0,0,1,0]
=> [1,1,0,1,1,1,0,0,0,1,0,0]
=> ? = 3
[1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,0,0,1,0,0,1,0]
=> [1,1,0,1,1,0,0,0,1,1,0,0]
=> ? = 3
[1,1,0,0,1,1,0,1,0,0]
=> [1,1,1,0,0,1,1,0,1,0,0,0]
=> [1,0,1,1,0,1,1,0,0,0,1,0]
=> [1,1,0,0,1,1,1,0,0,1,0,0]
=> ? = 3
[1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> [1,0,1,1,0,1,0,1,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,1,0,0]
=> ? = 2
[1,1,0,1,0,0,1,0,1,0]
=> [1,1,1,0,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,1,0,0]
=> [1,1,0,1,1,0,0,1,0,0,1,0]
=> ? = 2
[1,1,0,1,0,0,1,1,0,0]
=> [1,1,1,0,1,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,1,0,0]
=> [1,1,0,0,1,0,1,1,0,0,1,0]
=> ? = 2
[1,1,0,1,0,1,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,1,0,0,0]
=> [1,1,0,0,1,1,0,1,1,0,0,0]
=> ? = 3
[1,1,0,1,0,1,0,1,0,0]
=> [1,1,1,0,1,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,1,0,1,0,0,0]
=> ? = 3
[1,1,0,1,0,1,1,0,0,0]
=> [1,1,1,0,1,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,1,0,1,0,0,0]
=> [1,1,0,1,0,1,1,1,0,0,0,0]
=> ? = 3
[1,1,0,1,1,0,0,0,1,0]
=> [1,1,1,0,1,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,1,0,0]
=> [1,1,0,0,1,1,0,0,1,0,1,0]
=> ? = 2
[1,1,0,1,1,0,0,1,0,0]
=> [1,1,1,0,1,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,1,0,0]
=> [1,1,0,1,0,1,1,0,0,0,1,0]
=> ? = 3
[1,1,0,1,1,0,1,0,0,0]
=> [1,1,1,0,1,1,0,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,1,0,0,0]
=> [1,1,0,1,0,0,1,1,1,0,0,0]
=> ? = 3
[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]
=> [1,1,0,1,0,0,1,0,1,0,1,0]
=> ? = 2
[1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,1,0,0,0,1,0,1,0,0]
=> [1,0,1,1,1,0,0,0,1,0,1,0]
=> [1,1,0,1,1,0,0,1,0,1,0,0]
=> ? = 4
[1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> [1,0,1,1,0,1,0,0,1,0,1,0]
=> [1,1,0,0,1,0,1,1,0,1,0,0]
=> ? = 3
[1,1,1,0,0,1,0,0,1,0]
=> [1,1,1,1,0,0,1,0,0,1,0,0]
=> [1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,0,1,1,0,0]
=> ? = 3
[1,1,1,0,0,1,0,1,0,0]
=> [1,1,1,1,0,0,1,0,1,0,0,0]
=> [1,0,1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,0]
=> ? = 4
[1,1,1,0,0,1,1,0,0,0]
=> [1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,0,1,0,1,1,0,0]
=> ? = 3
[1,1,1,0,1,0,0,0,1,0]
=> [1,1,1,1,0,1,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,1,0,0]
=> [1,1,0,0,1,1,0,1,0,0,1,0]
=> ? = 2
[1,1,1,0,1,0,0,1,0,0]
=> [1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,0,1,1,0,0,1,0]
=> ? = 3
[1,1,1,0,1,0,1,0,0,0]
=> [1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,0,0,0]
=> ? = 4
[1,1,1,0,1,1,0,0,0,0]
=> [1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,0,1,0,1,0]
=> ? = 3
[1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> [1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,1,0,1,0,0]
=> ? = 4
[1,1,1,1,0,0,0,1,0,0]
=> [1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,0,1,1,0,1,0,0]
=> ? = 4
[1,1,1,1,0,0,1,0,0,0]
=> [1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,0,1,1,0,0]
=> ? = 4
[1,1,1,1,0,1,0,0,0,0]
=> [1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,0,1,0]
=> ? = 4
[1,1,1,1,1,0,0,0,0,0]
=> [1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,0]
=> ? = 5
[1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=> ? = 3
[1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=> [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> ? = 3
[1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=> [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=> ? = 3
[1,0,1,0,1,0,1,1,0,1,0,0]
=> [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=> [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=> [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=> ? = 3
[1,0,1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=> [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=> [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=> ? = 3
[1,0,1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=> [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=> [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=> ? = 3
[1,0,1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=> [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=> [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=> ? = 3
[1,0,1,0,1,1,0,1,0,0,1,0]
=> [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=> [1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=> ? = 3
Description
The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path.
The statistic returns zero in case that bimodule is the zero module.
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