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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000237
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Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
St000237: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00239: Permutations —Corteel⟶ Permutations
St000237: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
=> [1] => [1] => 0
[1,0,1,0]
=> [1,2] => [1,2] => 0
[1,1,0,0]
=> [2,1] => [2,1] => 1
[1,0,1,0,1,0]
=> [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0]
=> [1,3,2] => [1,3,2] => 1
[1,1,0,0,1,0]
=> [2,1,3] => [2,1,3] => 1
[1,1,0,1,0,0]
=> [2,3,1] => [3,2,1] => 0
[1,1,1,0,0,0]
=> [3,2,1] => [2,3,1] => 2
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2,4] => 1
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,3,2] => 0
[1,0,1,1,1,0,0,0]
=> [1,4,3,2] => [1,3,4,2] => 2
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => 2
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [3,2,1,4] => 0
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [4,2,3,1] => 0
[1,1,0,1,1,0,0,0]
=> [2,4,3,1] => [3,2,4,1] => 1
[1,1,1,0,0,0,1,0]
=> [3,2,1,4] => [2,3,1,4] => 2
[1,1,1,0,0,1,0,0]
=> [3,2,4,1] => [2,4,3,1] => 1
[1,1,1,0,1,0,0,0]
=> [4,2,3,1] => [2,3,4,1] => 3
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => [3,4,1,2] => 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,5,4,3] => 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => [1,2,4,5,3] => 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,4,3,2,5] => 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,3,4,2] => 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => [1,4,3,5,2] => 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => [1,3,4,2,5] => 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => [1,3,5,4,2] => 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => [1,3,4,5,2] => 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => [1,4,5,2,3] => 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,4,3] => 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => [2,1,4,5,3] => 3
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [3,2,1,4,5] => 0
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [3,2,1,5,4] => 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [4,2,3,1,5] => 0
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [5,2,3,4,1] => 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => [4,2,3,5,1] => 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => [3,2,4,1,5] => 1
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => [3,2,5,4,1] => 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => [3,2,4,5,1] => 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => [4,2,5,1,3] => 0
Description
The number of small exceedances.
This is the number of indices $i$ such that $\pi_i=i+1$.
Matching statistic: St000502
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000502: Set partitions ⟶ ℤResult quality: 68% ●values known / values provided: 68%●distinct values known / distinct values provided: 73%
Mp00239: Permutations —Corteel⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000502: Set partitions ⟶ ℤResult quality: 68% ●values known / values provided: 68%●distinct values known / distinct values provided: 73%
Values
[1,0]
=> [1] => [1] => {{1}}
=> ? = 0
[1,0,1,0]
=> [1,2] => [1,2] => {{1},{2}}
=> 0
[1,1,0,0]
=> [2,1] => [2,1] => {{1,2}}
=> 1
[1,0,1,0,1,0]
=> [1,2,3] => [1,2,3] => {{1},{2},{3}}
=> 0
[1,0,1,1,0,0]
=> [1,3,2] => [1,3,2] => {{1},{2,3}}
=> 1
[1,1,0,0,1,0]
=> [2,1,3] => [2,1,3] => {{1,2},{3}}
=> 1
[1,1,0,1,0,0]
=> [2,3,1] => [3,2,1] => {{1,3},{2}}
=> 0
[1,1,1,0,0,0]
=> [3,2,1] => [2,3,1] => {{1,2,3}}
=> 2
[1,0,1,0,1,0,1,0]
=> [1,2,3,4] => [1,2,3,4] => {{1},{2},{3},{4}}
=> 0
[1,0,1,0,1,1,0,0]
=> [1,2,4,3] => [1,2,4,3] => {{1},{2},{3,4}}
=> 1
[1,0,1,1,0,0,1,0]
=> [1,3,2,4] => [1,3,2,4] => {{1},{2,3},{4}}
=> 1
[1,0,1,1,0,1,0,0]
=> [1,3,4,2] => [1,4,3,2] => {{1},{2,4},{3}}
=> 0
[1,0,1,1,1,0,0,0]
=> [1,4,3,2] => [1,3,4,2] => {{1},{2,3,4}}
=> 2
[1,1,0,0,1,0,1,0]
=> [2,1,3,4] => [2,1,3,4] => {{1,2},{3},{4}}
=> 1
[1,1,0,0,1,1,0,0]
=> [2,1,4,3] => [2,1,4,3] => {{1,2},{3,4}}
=> 2
[1,1,0,1,0,0,1,0]
=> [2,3,1,4] => [3,2,1,4] => {{1,3},{2},{4}}
=> 0
[1,1,0,1,0,1,0,0]
=> [2,3,4,1] => [4,2,3,1] => {{1,4},{2},{3}}
=> 0
[1,1,0,1,1,0,0,0]
=> [2,4,3,1] => [3,2,4,1] => {{1,3,4},{2}}
=> 1
[1,1,1,0,0,0,1,0]
=> [3,2,1,4] => [2,3,1,4] => {{1,2,3},{4}}
=> 2
[1,1,1,0,0,1,0,0]
=> [3,2,4,1] => [2,4,3,1] => {{1,2,4},{3}}
=> 1
[1,1,1,0,1,0,0,0]
=> [4,2,3,1] => [2,3,4,1] => {{1,2,3,4}}
=> 3
[1,1,1,1,0,0,0,0]
=> [4,3,2,1] => [3,4,1,2] => {{1,3},{2,4}}
=> 0
[1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}}
=> 0
[1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,5,4] => [1,2,3,5,4] => {{1},{2},{3},{4,5}}
=> 1
[1,0,1,0,1,1,0,0,1,0]
=> [1,2,4,3,5] => [1,2,4,3,5] => {{1},{2},{3,4},{5}}
=> 1
[1,0,1,0,1,1,0,1,0,0]
=> [1,2,4,5,3] => [1,2,5,4,3] => {{1},{2},{3,5},{4}}
=> 0
[1,0,1,0,1,1,1,0,0,0]
=> [1,2,5,4,3] => [1,2,4,5,3] => {{1},{2},{3,4,5}}
=> 2
[1,0,1,1,0,0,1,0,1,0]
=> [1,3,2,4,5] => [1,3,2,4,5] => {{1},{2,3},{4},{5}}
=> 1
[1,0,1,1,0,0,1,1,0,0]
=> [1,3,2,5,4] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
=> 2
[1,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,5] => [1,4,3,2,5] => {{1},{2,4},{3},{5}}
=> 0
[1,0,1,1,0,1,0,1,0,0]
=> [1,3,4,5,2] => [1,5,3,4,2] => {{1},{2,5},{3},{4}}
=> 0
[1,0,1,1,0,1,1,0,0,0]
=> [1,3,5,4,2] => [1,4,3,5,2] => {{1},{2,4,5},{3}}
=> 1
[1,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,5] => [1,3,4,2,5] => {{1},{2,3,4},{5}}
=> 2
[1,0,1,1,1,0,0,1,0,0]
=> [1,4,3,5,2] => [1,3,5,4,2] => {{1},{2,3,5},{4}}
=> 1
[1,0,1,1,1,0,1,0,0,0]
=> [1,5,3,4,2] => [1,3,4,5,2] => {{1},{2,3,4,5}}
=> 3
[1,0,1,1,1,1,0,0,0,0]
=> [1,5,4,3,2] => [1,4,5,2,3] => {{1},{2,4},{3,5}}
=> 0
[1,1,0,0,1,0,1,0,1,0]
=> [2,1,3,4,5] => [2,1,3,4,5] => {{1,2},{3},{4},{5}}
=> 1
[1,1,0,0,1,0,1,1,0,0]
=> [2,1,3,5,4] => [2,1,3,5,4] => {{1,2},{3},{4,5}}
=> 2
[1,1,0,0,1,1,0,0,1,0]
=> [2,1,4,3,5] => [2,1,4,3,5] => {{1,2},{3,4},{5}}
=> 2
[1,1,0,0,1,1,0,1,0,0]
=> [2,1,4,5,3] => [2,1,5,4,3] => {{1,2},{3,5},{4}}
=> 1
[1,1,0,0,1,1,1,0,0,0]
=> [2,1,5,4,3] => [2,1,4,5,3] => {{1,2},{3,4,5}}
=> 3
[1,1,0,1,0,0,1,0,1,0]
=> [2,3,1,4,5] => [3,2,1,4,5] => {{1,3},{2},{4},{5}}
=> 0
[1,1,0,1,0,0,1,1,0,0]
=> [2,3,1,5,4] => [3,2,1,5,4] => {{1,3},{2},{4,5}}
=> 1
[1,1,0,1,0,1,0,0,1,0]
=> [2,3,4,1,5] => [4,2,3,1,5] => {{1,4},{2},{3},{5}}
=> 0
[1,1,0,1,0,1,0,1,0,0]
=> [2,3,4,5,1] => [5,2,3,4,1] => {{1,5},{2},{3},{4}}
=> 0
[1,1,0,1,0,1,1,0,0,0]
=> [2,3,5,4,1] => [4,2,3,5,1] => {{1,4,5},{2},{3}}
=> 1
[1,1,0,1,1,0,0,0,1,0]
=> [2,4,3,1,5] => [3,2,4,1,5] => {{1,3,4},{2},{5}}
=> 1
[1,1,0,1,1,0,0,1,0,0]
=> [2,4,3,5,1] => [3,2,5,4,1] => {{1,3,5},{2},{4}}
=> 0
[1,1,0,1,1,0,1,0,0,0]
=> [2,5,3,4,1] => [3,2,4,5,1] => {{1,3,4,5},{2}}
=> 2
[1,1,0,1,1,1,0,0,0,0]
=> [2,5,4,3,1] => [4,2,5,1,3] => {{1,4},{2},{3,5}}
=> 0
[1,1,1,0,0,0,1,0,1,0]
=> [3,2,1,4,5] => [2,3,1,4,5] => {{1,2,3},{4},{5}}
=> 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => {{1},{2},{3},{4},{5},{6},{7},{8}}
=> ? = 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [1,2,3,4,5,6,8,7] => [1,2,3,4,5,6,8,7] => {{1},{2},{3},{4},{5},{6},{7,8}}
=> ? = 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=> [1,2,3,4,5,7,6,8] => [1,2,3,4,5,7,6,8] => {{1},{2},{3},{4},{5},{6,7},{8}}
=> ? = 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=> [1,2,3,5,4,6,7,8] => [1,2,3,5,4,6,7,8] => {{1},{2},{3},{4,5},{6},{7},{8}}
=> ? = 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=> [1,2,3,5,4,7,6,8] => [1,2,3,5,4,7,6,8] => {{1},{2},{3},{4,5},{6,7},{8}}
=> ? = 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=> [1,2,3,8,5,6,7,4] => [1,2,3,5,6,7,8,4] => {{1},{2},{3},{4,5,6,7,8}}
=> ? = 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=> [1,2,4,3,6,5,7,8] => [1,2,4,3,6,5,7,8] => {{1},{2},{3,4},{5,6},{7},{8}}
=> ? = 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=> [1,2,6,5,4,3,7,8] => [1,2,5,6,3,4,7,8] => {{1},{2},{3,5},{4,6},{7},{8}}
=> ? = 0
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [1,3,2,4,5,6,7,8] => [1,3,2,4,5,6,7,8] => {{1},{2,3},{4},{5},{6},{7},{8}}
=> ? = 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=> [1,3,2,4,5,7,6,8] => [1,3,2,4,5,7,6,8] => {{1},{2,3},{4},{5},{6,7},{8}}
=> ? = 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=> [1,3,2,5,4,6,7,8] => [1,3,2,5,4,6,7,8] => {{1},{2,3},{4,5},{6},{7},{8}}
=> ? = 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=> [1,3,2,5,4,7,6,8] => [1,3,2,5,4,7,6,8] => {{1},{2,3},{4,5},{6,7},{8}}
=> ? = 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
=> [1,3,4,2,6,7,5,8] => [1,4,3,2,7,6,5,8] => {{1},{2,4},{3},{5,7},{6},{8}}
=> ? = 0
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=> [1,3,5,4,7,6,8,2] => [1,4,3,6,5,8,7,2] => {{1},{2,4,6,8},{3},{5},{7}}
=> ? = 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
=> [1,3,6,5,4,7,2,8] => [1,5,3,7,2,6,4,8] => {{1},{2,5},{3},{4,7},{6},{8}}
=> ? = 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=> [1,4,3,2,7,6,5,8] => [1,3,4,2,6,7,5,8] => {{1},{2,3,4},{5,6,7},{8}}
=> ? = 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=> [1,7,3,5,4,6,2,8] => [1,3,5,6,2,7,4,8] => {{1},{2,3,5},{4,6,7},{8}}
=> ? = 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=> [1,7,6,4,5,3,2,8] => [1,4,5,6,7,2,3,8] => {{1},{2,4,6},{3,5,7},{8}}
=> ? = 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=> [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => {{1,2},{3},{4},{5},{6},{7},{8}}
=> ? = 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
=> [2,1,3,4,5,6,8,7] => [2,1,3,4,5,6,8,7] => {{1,2},{3},{4},{5},{6},{7,8}}
=> ? = 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
=> [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => {{1,2},{3,4},{5,6},{7,8}}
=> ? = 4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
=> [2,1,4,3,6,8,7,5] => [2,1,4,3,7,6,8,5] => {{1,2},{3,4},{5,7,8},{6}}
=> ? = 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
=> [2,1,4,3,7,6,8,5] => [2,1,4,3,6,8,7,5] => {{1,2},{3,4},{5,6,8},{7}}
=> ? = 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
=> [2,1,4,3,8,7,6,5] => [2,1,4,3,7,8,5,6] => {{1,2},{3,4},{5,7},{6,8}}
=> ? = 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
=> [2,1,4,6,5,3,8,7] => [2,1,5,4,6,3,8,7] => {{1,2},{3,5,6},{4},{7,8}}
=> ? = 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
=> [2,1,4,6,5,8,7,3] => [2,1,5,4,7,6,8,3] => {{1,2},{3,5,7,8},{4},{6}}
=> ? = 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
=> [2,1,4,8,6,5,7,3] => [2,1,6,4,7,3,8,5] => {{1,2},{3,6},{4},{5,7,8}}
=> ? = 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
=> [2,1,5,4,6,3,8,7] => [2,1,4,6,5,3,8,7] => {{1,2},{3,4,6},{5},{7,8}}
=> ? = 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
=> [2,1,6,4,5,7,8,3] => [2,1,4,5,8,6,7,3] => {{1,2},{3,4,5,8},{6},{7}}
=> ? = 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,1,6,5,4,3,8,7] => [2,1,5,6,3,4,8,7] => {{1,2},{3,5},{4,6},{7,8}}
=> ? = 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
=> [2,1,8,5,4,7,6,3] => [2,1,5,7,3,8,4,6] => {{1,2},{3,5},{4,7},{6,8}}
=> ? = 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,1,8,7,6,5,4,3] => [2,1,6,7,8,3,4,5] => {{1,2},{3,6},{4,7},{5,8}}
=> ? = 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [2,3,1,4,5,6,7,8] => [3,2,1,4,5,6,7,8] => {{1,3},{2},{4},{5},{6},{7},{8}}
=> ? = 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
=> [2,3,1,4,5,7,8,6] => [3,2,1,4,5,8,7,6] => {{1,3},{2},{4},{5},{6,8},{7}}
=> ? = 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]
=> [2,3,1,5,7,6,8,4] => [3,2,1,6,5,8,7,4] => {{1,3},{2},{4,6,8},{5},{7}}
=> ? = 0
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]
=> [2,3,4,1,6,7,8,5] => [4,2,3,1,8,6,7,5] => {{1,4},{2},{3},{5,8},{6},{7}}
=> ? = 0
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]
=> [2,3,4,8,5,6,7,1] => [5,2,3,4,6,7,8,1] => {{1,5,6,7,8},{2},{3},{4}}
=> ? = 3
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]
=> [2,3,6,5,4,7,8,1] => [5,2,3,8,1,6,7,4] => {{1,5},{2},{3},{4,8},{6},{7}}
=> ? = 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]
=> [2,4,3,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => {{1,3,4},{2},{5,6},{7,8}}
=> ? = 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]
=> [2,4,3,1,6,8,7,5] => [3,2,4,1,7,6,8,5] => {{1,3,4},{2},{5,7,8},{6}}
=> ? = 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]
=> [2,4,3,1,7,6,8,5] => [3,2,4,1,6,8,7,5] => {{1,3,4},{2},{5,6,8},{7}}
=> ? = 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]
=> [2,4,3,5,1,7,8,6] => [3,2,5,4,1,8,7,6] => {{1,3,5},{2},{4},{6,8},{7}}
=> ? = 0
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]
=> [2,4,3,6,5,1,8,7] => [3,2,5,4,6,1,8,7] => {{1,3,5,6},{2},{4},{7,8}}
=> ? = 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]
=> [2,4,3,6,5,7,1,8] => [3,2,5,4,7,6,1,8] => {{1,3,5,7},{2},{4},{6},{8}}
=> ? = 0
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]
=> [2,4,3,6,5,8,7,1] => [3,2,5,4,7,6,8,1] => {{1,3,5,7,8},{2},{4},{6}}
=> ? = 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]
=> [2,7,3,5,4,6,8,1] => [3,2,5,6,1,8,7,4] => {{1,3,5},{2},{4,6,8},{7}}
=> ? = 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]
=> [2,5,4,3,1,6,7,8] => [4,2,5,1,3,6,7,8] => {{1,4},{2},{3,5},{6},{7},{8}}
=> ? = 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]
=> [2,6,4,3,5,1,8,7] => [4,2,5,1,6,3,8,7] => {{1,4},{2},{3,5,6},{7,8}}
=> ? = 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]
=> [2,7,6,4,5,3,8,1] => [4,2,5,6,8,1,7,3] => {{1,4,6},{2},{3,5,8},{7}}
=> ? = 0
Description
The number of successions of a set partitions.
This is the number of indices $i$ such that $i$ and $i+1$ belonging to the same block.
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