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Matching statistic: St000223
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000223: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St000223: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
=> [1] => [1,0]
=> [2,1] => 0
{{1,2}}
=> [2,1] => [1,1,0,0]
=> [2,3,1] => 0
{{1},{2}}
=> [1,2] => [1,0,1,0]
=> [3,1,2] => 0
{{1,2,3}}
=> [2,3,1] => [1,1,0,1,0,0]
=> [4,3,1,2] => 1
{{1,2},{3}}
=> [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,1,1,0,0,0]
=> [2,3,4,1] => 0
{{1},{2,3}}
=> [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => 1
{{1,2,3},{4}}
=> [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => 1
{{1,2,4},{3}}
=> [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => 1
{{1,2},{3,4}}
=> [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => 1
{{1,3},{2,4}}
=> [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => 0
{{1,4},{2,3}}
=> [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 0
{{1},{2,3,4}}
=> [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 0
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => 0
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 0
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => 2
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => 2
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => 0
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => 2
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> [6,5,4,1,2,3] => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0]
=> [6,3,5,1,2,4] => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => 2
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => 0
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => 0
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,1,4] => 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> [2,6,4,5,1,3] => 2
Description
The number of nestings in the permutation.
Matching statistic: St001513
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001513: Permutations ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 57%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001513: Permutations ⟶ ℤResult quality: 22% ●values known / values provided: 22%●distinct values known / distinct values provided: 57%
Values
{{1}}
=> [1] => [1,0]
=> [2,1] => 0
{{1,2}}
=> [2,1] => [1,1,0,0]
=> [2,3,1] => 0
{{1},{2}}
=> [1,2] => [1,0,1,0]
=> [3,1,2] => 0
{{1,2,3}}
=> [2,3,1] => [1,1,0,1,0,0]
=> [4,3,1,2] => 1
{{1,2},{3}}
=> [2,1,3] => [1,1,0,0,1,0]
=> [2,4,1,3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,1,1,0,0,0]
=> [2,3,4,1] => 0
{{1},{2,3}}
=> [1,3,2] => [1,0,1,1,0,0]
=> [3,1,4,2] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,0,1,0,1,0]
=> [4,1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [5,4,1,2,3] => 1
{{1,2,3},{4}}
=> [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => 1
{{1,2,4},{3}}
=> [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> [4,3,1,5,2] => 1
{{1,2},{3,4}}
=> [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [2,5,1,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [2,5,4,1,3] => 1
{{1,3},{2,4}}
=> [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [5,3,4,1,2] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => 0
{{1,4},{2,3}}
=> [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 0
{{1},{2,3,4}}
=> [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => 1
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [3,1,5,2,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [2,3,4,5,1] => 0
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => 0
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [4,1,2,5,3] => 0
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [5,1,2,3,4] => 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [5,6,1,2,3,4] => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [6,4,1,2,3,5] => 1
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
=> [5,4,1,2,6,3] => 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [5,3,1,2,6,4] => 1
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [6,3,1,2,4,5] => 1
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
=> [6,3,1,5,2,4] => 2
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> [6,4,1,5,2,3] => 2
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
=> [4,3,1,6,2,5] => 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => 1
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> [2,6,1,5,3,4] => 1
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [2,4,1,6,3,5] => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0]
=> [4,3,1,5,6,2] => 1
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [2,4,1,5,6,3] => 0
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [2,5,1,3,6,4] => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [2,6,1,3,4,5] => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
=> [2,6,5,1,3,4] => 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => 2
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> [2,6,4,1,3,5] => 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> [6,5,4,1,2,3] => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0]
=> [6,3,5,1,2,4] => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> [6,3,4,1,2,5] => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
=> [2,5,4,1,6,3] => 1
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> [5,3,4,1,6,2] => 2
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> [2,3,5,1,6,4] => 0
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [2,3,6,1,4,5] => 0
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [2,3,6,5,1,4] => 1
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> [2,6,4,5,1,3] => 2
{{1,2,3,4,5,6}}
=> [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0]
=> [7,6,1,2,3,4,5] => ? = 1
{{1,2,3,4,6},{5}}
=> [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0]
=> [5,6,1,2,3,7,4] => ? = 0
{{1,2,3,4},{5},{6}}
=> [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0]
=> [7,4,1,2,3,5,6] => ? = 1
{{1,2,3},{4},{5},{6}}
=> [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0]
=> [7,3,1,2,4,5,6] => ? = 1
{{1,2},{3},{4},{5},{6}}
=> [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0]
=> [2,7,1,3,4,5,6] => ? = 0
{{1,3,4,5,6},{2}}
=> [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0]
=> [2,6,7,1,3,4,5] => ? = 0
{{1,3},{2,4},{5},{6}}
=> [3,4,1,2,5,6] => [1,1,1,0,1,0,0,0,1,0,1,0]
=> [7,3,4,1,2,5,6] => ? = 2
{{1,4},{2,3},{5,6}}
=> [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,3,4,6,1,7,5] => ? = 0
{{1,4},{2,3},{5},{6}}
=> [4,3,2,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
=> [2,3,4,7,1,5,6] => ? = 0
{{1,5},{2,3,4},{6}}
=> [5,3,4,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 0
{{1,6},{2,3,4,5}}
=> [6,3,4,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2,3,4},{5}}
=> [6,3,4,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,5},{2,3},{4},{6}}
=> [5,3,2,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 0
{{1,6},{2,3,5},{4}}
=> [6,3,5,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2,3},{4,5}}
=> [6,3,2,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2,3},{4},{5}}
=> [6,3,2,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,4},{2,5},{3,6}}
=> [4,5,6,1,2,3] => [1,1,1,1,0,1,0,1,0,0,0,0]
=> [7,6,4,5,1,2,3] => ? = 5
{{1,4},{2},{3},{5,6}}
=> [4,2,3,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0]
=> [2,3,4,6,1,7,5] => ? = 0
{{1,4},{2},{3},{5},{6}}
=> [4,2,3,1,5,6] => [1,1,1,1,0,0,0,0,1,0,1,0]
=> [2,3,4,7,1,5,6] => ? = 0
{{1,5},{2,4},{3},{6}}
=> [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 0
{{1,6},{2,4,5},{3}}
=> [6,4,3,5,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2,4},{3,5}}
=> [6,4,5,2,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2,4},{3},{5}}
=> [6,4,3,2,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,5},{2},{3,4},{6}}
=> [5,2,4,3,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 0
{{1,6},{2,5},{3,4}}
=> [6,5,4,3,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2},{3,4,5}}
=> [6,2,4,5,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2},{3,4},{5}}
=> [6,2,4,3,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,5},{2},{3},{4},{6}}
=> [5,2,3,4,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
=> [2,3,4,5,7,1,6] => ? = 0
{{1,6},{2,5},{3},{4}}
=> [6,5,3,4,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2},{3,5},{4}}
=> [6,2,5,4,3,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1,6},{2},{3},{4,5}}
=> [6,2,3,5,4,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1},{2},{3},{4,5},{6}}
=> [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0]
=> [5,1,2,3,7,4,6] => ? = 0
{{1,6},{2},{3},{4},{5}}
=> [6,2,3,4,5,1] => [1,1,1,1,1,1,0,0,0,0,0,0]
=> [2,3,4,5,6,7,1] => ? = 0
{{1},{2},{3},{4,6},{5}}
=> [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0]
=> [5,1,2,3,6,7,4] => ? = 0
{{1},{2},{3},{4},{5,6}}
=> [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0]
=> [6,1,2,3,4,7,5] => ? = 0
{{1},{2},{3},{4},{5},{6}}
=> [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0]
=> [7,1,2,3,4,5,6] => ? = 0
{{1,2,3,4,5,6,7}}
=> [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=> [8,7,1,2,3,4,5,6] => ? = 1
{{1,2,3,4},{5},{6},{7}}
=> [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=> [8,4,1,2,3,5,6,7] => ? = 1
{{1,2,3},{4},{5,6,7}}
=> [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0]
=> [8,3,1,2,4,7,5,6] => ? = 2
{{1,2,3},{4},{5},{6},{7}}
=> [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=> [8,3,1,2,4,5,6,7] => ? = 1
{{1,2,5},{3,4,6},{7}}
=> [2,5,4,6,1,3,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [8,3,1,5,6,2,4,7] => ? = 3
{{1,2,5},{3},{4,6},{7}}
=> [2,5,3,6,1,4,7] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=> [8,3,1,5,6,2,4,7] => ? = 3
{{1,2},{3},{4},{5},{6},{7}}
=> [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=> [2,8,1,3,4,5,6,7] => ? = 0
{{1,3,4,5,7},{2,6}}
=> [3,6,4,5,7,2,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [8,3,4,1,6,7,2,5] => ? = 4
{{1,3,4,5,7},{2},{6}}
=> [3,2,4,5,7,6,1] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=> [2,6,7,1,3,4,8,5] => ? = 0
{{1,3,4},{2,6},{5,7}}
=> [3,6,4,1,7,2,5] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [8,3,4,1,6,7,2,5] => ? = 4
{{1,3,5,7},{2,4,6}}
=> [3,4,5,6,7,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=> [6,7,8,1,2,3,4,5] => ? = 0
{{1,3},{2,4,6},{5,7}}
=> [3,4,1,6,7,2,5] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=> [6,3,8,1,2,7,4,5] => ? = 2
{{1,3,5,7},{2,6},{4}}
=> [3,6,5,4,7,2,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=> [8,3,4,1,6,7,2,5] => ? = 4
{{1,3,6},{2,5,7},{4}}
=> [3,5,6,4,7,1,2] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=> [7,8,4,1,6,2,3,5] => ? = 4
Description
The number of nested exceedences of a permutation.
For a permutation $\pi$, this is the number of pairs $i,j$ such that $i < j < \pi(j) < \pi(i)$. For exceedences, see [[St000155]].
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