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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001438
Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
St001438: Skew partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00172: Integer compositions —rotate back to front⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
St001438: Skew partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
=> [1] => [1] => [[1],[]]
=> 0
{{1,2}}
=> [2] => [2] => [[2],[]]
=> 0
{{1},{2}}
=> [1,1] => [1,1] => [[1,1],[]]
=> 0
{{1,2,3}}
=> [3] => [3] => [[3],[]]
=> 0
{{1,2},{3}}
=> [2,1] => [1,2] => [[2,1],[]]
=> 0
{{1,3},{2}}
=> [2,1] => [1,2] => [[2,1],[]]
=> 0
{{1},{2,3}}
=> [1,2] => [2,1] => [[2,2],[1]]
=> 1
{{1},{2},{3}}
=> [1,1,1] => [1,1,1] => [[1,1,1],[]]
=> 0
{{1,2,3,4}}
=> [4] => [4] => [[4],[]]
=> 0
{{1,2,3},{4}}
=> [3,1] => [1,3] => [[3,1],[]]
=> 0
{{1,2,4},{3}}
=> [3,1] => [1,3] => [[3,1],[]]
=> 0
{{1,2},{3,4}}
=> [2,2] => [2,2] => [[3,2],[1]]
=> 1
{{1,2},{3},{4}}
=> [2,1,1] => [1,2,1] => [[2,2,1],[1]]
=> 1
{{1,3,4},{2}}
=> [3,1] => [1,3] => [[3,1],[]]
=> 0
{{1,3},{2,4}}
=> [2,2] => [2,2] => [[3,2],[1]]
=> 1
{{1,3},{2},{4}}
=> [2,1,1] => [1,2,1] => [[2,2,1],[1]]
=> 1
{{1,4},{2,3}}
=> [2,2] => [2,2] => [[3,2],[1]]
=> 1
{{1},{2,3,4}}
=> [1,3] => [3,1] => [[3,3],[2]]
=> 2
{{1},{2,3},{4}}
=> [1,2,1] => [1,1,2] => [[2,1,1],[]]
=> 0
{{1,4},{2},{3}}
=> [2,1,1] => [1,2,1] => [[2,2,1],[1]]
=> 1
{{1},{2,4},{3}}
=> [1,2,1] => [1,1,2] => [[2,1,1],[]]
=> 0
{{1},{2},{3,4}}
=> [1,1,2] => [2,1,1] => [[2,2,2],[1,1]]
=> 2
{{1},{2},{3},{4}}
=> [1,1,1,1] => [1,1,1,1] => [[1,1,1,1],[]]
=> 0
{{1,2,3,4,5}}
=> [5] => [5] => [[5],[]]
=> 0
{{1,2,3,4},{5}}
=> [4,1] => [1,4] => [[4,1],[]]
=> 0
{{1,2,3,5},{4}}
=> [4,1] => [1,4] => [[4,1],[]]
=> 0
{{1,2,3},{4,5}}
=> [3,2] => [2,3] => [[4,2],[1]]
=> 1
{{1,2,3},{4},{5}}
=> [3,1,1] => [1,3,1] => [[3,3,1],[2]]
=> 2
{{1,2,4,5},{3}}
=> [4,1] => [1,4] => [[4,1],[]]
=> 0
{{1,2,4},{3,5}}
=> [3,2] => [2,3] => [[4,2],[1]]
=> 1
{{1,2,4},{3},{5}}
=> [3,1,1] => [1,3,1] => [[3,3,1],[2]]
=> 2
{{1,2,5},{3,4}}
=> [3,2] => [2,3] => [[4,2],[1]]
=> 1
{{1,2},{3,4,5}}
=> [2,3] => [3,2] => [[4,3],[2]]
=> 2
{{1,2},{3,4},{5}}
=> [2,2,1] => [1,2,2] => [[3,2,1],[1]]
=> 1
{{1,2,5},{3},{4}}
=> [3,1,1] => [1,3,1] => [[3,3,1],[2]]
=> 2
{{1,2},{3,5},{4}}
=> [2,2,1] => [1,2,2] => [[3,2,1],[1]]
=> 1
{{1,2},{3},{4,5}}
=> [2,1,2] => [2,2,1] => [[3,3,2],[2,1]]
=> 3
{{1,2},{3},{4},{5}}
=> [2,1,1,1] => [1,2,1,1] => [[2,2,2,1],[1,1]]
=> 2
{{1,3,4,5},{2}}
=> [4,1] => [1,4] => [[4,1],[]]
=> 0
{{1,3,4},{2,5}}
=> [3,2] => [2,3] => [[4,2],[1]]
=> 1
{{1,3,4},{2},{5}}
=> [3,1,1] => [1,3,1] => [[3,3,1],[2]]
=> 2
{{1,3,5},{2,4}}
=> [3,2] => [2,3] => [[4,2],[1]]
=> 1
{{1,3},{2,4,5}}
=> [2,3] => [3,2] => [[4,3],[2]]
=> 2
{{1,3},{2,4},{5}}
=> [2,2,1] => [1,2,2] => [[3,2,1],[1]]
=> 1
{{1,3,5},{2},{4}}
=> [3,1,1] => [1,3,1] => [[3,3,1],[2]]
=> 2
{{1,3},{2,5},{4}}
=> [2,2,1] => [1,2,2] => [[3,2,1],[1]]
=> 1
{{1,3},{2},{4,5}}
=> [2,1,2] => [2,2,1] => [[3,3,2],[2,1]]
=> 3
{{1,3},{2},{4},{5}}
=> [2,1,1,1] => [1,2,1,1] => [[2,2,2,1],[1,1]]
=> 2
{{1,4,5},{2,3}}
=> [3,2] => [2,3] => [[4,2],[1]]
=> 1
{{1,4},{2,3,5}}
=> [2,3] => [3,2] => [[4,3],[2]]
=> 2
Description
The number of missing boxes of a skew partition.
Matching statistic: St001857
(load all 7 compositions to match this statistic)
(load all 7 compositions to match this statistic)
Mp00220: Set partitions —Yip⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 40%
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001857: Signed permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 40%
Values
{{1}}
=> {{1}}
=> [1] => [1] => 0
{{1,2}}
=> {{1,2}}
=> [2,1] => [2,1] => 0
{{1},{2}}
=> {{1},{2}}
=> [1,2] => [1,2] => 0
{{1,2,3}}
=> {{1,2,3}}
=> [2,3,1] => [2,3,1] => 0
{{1,2},{3}}
=> {{1,2},{3}}
=> [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
=> {{1},{2,3}}
=> [1,3,2] => [1,3,2] => 0
{{1},{2,3}}
=> {{1,3},{2}}
=> [3,2,1] => [3,2,1] => 1
{{1},{2},{3}}
=> {{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => ? = 0
{{1,2,3},{4}}
=> {{1,2,3},{4}}
=> [2,3,1,4] => [2,3,1,4] => ? = 0
{{1,2,4},{3}}
=> {{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => ? = 0
{{1,2},{3,4}}
=> {{1,2,4},{3}}
=> [2,4,3,1] => [2,4,3,1] => ? = 1
{{1,2},{3},{4}}
=> {{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => ? = 1
{{1,3,4},{2}}
=> {{1},{2,3,4}}
=> [1,3,4,2] => [1,3,4,2] => ? = 0
{{1,3},{2,4}}
=> {{1,4},{2,3}}
=> [4,3,2,1] => [4,3,2,1] => ? = 1
{{1,3},{2},{4}}
=> {{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => ? = 1
{{1,4},{2,3}}
=> {{1,3},{2,4}}
=> [3,4,1,2] => [3,4,1,2] => ? = 1
{{1},{2,3,4}}
=> {{1,3,4},{2}}
=> [3,2,4,1] => [3,2,4,1] => ? = 2
{{1},{2,3},{4}}
=> {{1,3},{2},{4}}
=> [3,2,1,4] => [3,2,1,4] => ? = 0
{{1,4},{2},{3}}
=> {{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => ? = 1
{{1},{2,4},{3}}
=> {{1},{2,4},{3}}
=> [1,4,3,2] => [1,4,3,2] => ? = 0
{{1},{2},{3,4}}
=> {{1,4},{2},{3}}
=> [4,2,3,1] => [4,2,3,1] => ? = 2
{{1},{2},{3},{4}}
=> {{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => ? = 0
{{1,2,3,4,5}}
=> {{1,2,3,4,5}}
=> [2,3,4,5,1] => [2,3,4,5,1] => ? = 0
{{1,2,3,4},{5}}
=> {{1,2,3,4},{5}}
=> [2,3,4,1,5] => [2,3,4,1,5] => ? = 0
{{1,2,3,5},{4}}
=> {{1,2,3},{4,5}}
=> [2,3,1,5,4] => [2,3,1,5,4] => ? = 0
{{1,2,3},{4,5}}
=> {{1,2,3,5},{4}}
=> [2,3,5,4,1] => [2,3,5,4,1] => ? = 1
{{1,2,3},{4},{5}}
=> {{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [2,3,1,4,5] => ? = 2
{{1,2,4,5},{3}}
=> {{1,2,5},{3,4}}
=> [2,5,4,3,1] => [2,5,4,3,1] => ? = 0
{{1,2,4},{3,5}}
=> {{1,2},{3,4,5}}
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 1
{{1,2,4},{3},{5}}
=> {{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [2,1,4,3,5] => ? = 2
{{1,2,5},{3,4}}
=> {{1,2,4},{3,5}}
=> [2,4,5,1,3] => [2,4,5,1,3] => ? = 1
{{1,2},{3,4,5}}
=> {{1,2,4,5},{3}}
=> [2,4,3,5,1] => [2,4,3,5,1] => ? = 2
{{1,2},{3,4},{5}}
=> {{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [2,4,3,1,5] => ? = 1
{{1,2,5},{3},{4}}
=> {{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [2,1,3,5,4] => ? = 2
{{1,2},{3,5},{4}}
=> {{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
{{1,2},{3},{4,5}}
=> {{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [2,5,3,4,1] => ? = 3
{{1,2},{3},{4},{5}}
=> {{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [2,1,3,4,5] => ? = 2
{{1,3,4,5},{2}}
=> {{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => ? = 0
{{1,3,4},{2,5}}
=> {{1,5},{2,3,4}}
=> [5,3,4,2,1] => [5,3,4,2,1] => ? = 1
{{1,3,4},{2},{5}}
=> {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,3,4,2,5] => ? = 2
{{1,3,5},{2,4}}
=> {{1,4},{2,3,5}}
=> [4,3,5,1,2] => [4,3,5,1,2] => ? = 1
{{1,3},{2,4,5}}
=> {{1,4,5},{2,3}}
=> [4,3,2,5,1] => [4,3,2,5,1] => ? = 2
{{1,3},{2,4},{5}}
=> {{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [4,3,2,1,5] => ? = 1
{{1,3,5},{2},{4}}
=> {{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [5,3,2,4,1] => ? = 2
{{1,3},{2,5},{4}}
=> {{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,3,2,5,4] => ? = 1
{{1,3},{2},{4,5}}
=> {{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,3,5,4,2] => ? = 3
{{1,3},{2},{4},{5}}
=> {{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => ? = 2
{{1,4,5},{2,3}}
=> {{1,3,5},{2,4}}
=> [3,4,5,2,1] => [3,4,5,2,1] => ? = 1
{{1,4},{2,3,5}}
=> {{1,3},{2,4,5}}
=> [3,4,1,5,2] => [3,4,1,5,2] => ? = 2
{{1,4},{2,3},{5}}
=> {{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [3,4,1,2,5] => ? = 1
{{1,5},{2,3,4}}
=> {{1,3,4},{2,5}}
=> [3,5,4,1,2] => [3,5,4,1,2] => ? = 2
{{1},{2,3,4,5}}
=> {{1,3,4,5},{2}}
=> [3,2,4,5,1] => [3,2,4,5,1] => ? = 3
{{1},{2,3,4},{5}}
=> {{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [3,2,4,1,5] => ? = 0
{{1,5},{2,3},{4}}
=> {{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [3,2,1,5,4] => ? = 1
{{1},{2,3,5},{4}}
=> {{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [3,5,1,4,2] => ? = 0
{{1},{2,3},{4,5}}
=> {{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [3,2,5,4,1] => ? = 2
{{1},{2,3},{4},{5}}
=> {{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [3,2,1,4,5] => ? = 1
Description
The number of edges in the reduced word graph of a signed permutation.
The reduced word graph of a signed permutation $\pi$ has the reduced words of $\pi$ as vertices and an edge between two reduced words if they differ by exactly one braid move.
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