Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000589
(load all 99 compositions to match this statistic)
Mapping
St000589: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => 0
{{1},{2}}
 => 0
{{1,2,3}}
 => 0
{{1,2},{3}}
 => 0
{{1,3},{2}}
 => 0
{{1},{2,3}}
 => 1
{{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => 0
{{1,2,4},{3}}
 => 0
{{1,2},{3,4}}
 => 1
{{1,2},{3},{4}}
 => 0
{{1,3,4},{2}}
 => 1
{{1,3},{2,4}}
 => 0
{{1,3},{2},{4}}
 => 0
{{1,4},{2,3}}
 => 0
{{1},{2,3,4}}
 => 2
{{1},{2,3},{4}}
 => 1
{{1,4},{2},{3}}
 => 0
{{1},{2,4},{3}}
 => 1
{{1},{2},{3,4}}
 => 2
{{1},{2},{3},{4}}
 => 0
{{1,2,3,4,5}}
 => 0
{{1,2,3,4},{5}}
 => 0
{{1,2,3,5},{4}}
 => 0
{{1,2,3},{4,5}}
 => 1
{{1,2,3},{4},{5}}
 => 0
{{1,2,4,5},{3}}
 => 1
{{1,2,4},{3,5}}
 => 0
{{1,2,4},{3},{5}}
 => 0
{{1,2,5},{3,4}}
 => 0
{{1,2},{3,4,5}}
 => 2
{{1,2},{3,4},{5}}
 => 1
{{1,2,5},{3},{4}}
 => 0
{{1,2},{3,5},{4}}
 => 1
{{1,2},{3},{4,5}}
 => 2
{{1,2},{3},{4},{5}}
 => 0
{{1,3,4,5},{2}}
 => 2
{{1,3,4},{2,5}}
 => 0
{{1,3,4},{2},{5}}
 => 1
{{1,3,5},{2,4}}
 => 0
{{1,3},{2,4,5}}
 => 1
{{1,3},{2,4},{5}}
 => 0
{{1,3,5},{2},{4}}
 => 1
{{1,3},{2,5},{4}}
 => 0
{{1,3},{2},{4,5}}
 => 2
{{1,3},{2},{4},{5}}
 => 0
{{1,4,5},{2,3}}
 => 1
{{1,4},{2,3,5}}
 => 0
{{1,4},{2,3},{5}}
 => 0
Description
The number of occurrences of the pattern {{1},{2,3}} such that 1 is maximal, (2,3) are consecutive in a block.
Matching statistic: St001867
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001867: Signed permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 45%
Values
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,1,2] => [3,1,2] => 0
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [3,2,1] => 0
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [3,1,2,4] => [3,1,2,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => [4,1,3,2] => 0
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [4,2,1,3] => [4,2,1,3] => 1
{{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => [3,4,1,2] => 0
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 0
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 0
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => [4,2,3,1] => 0
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => [1,4,3,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 2
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [5,1,2,3,4] => [5,1,2,3,4] => ? = 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [4,1,2,3,5] => [4,1,2,3,5] => ? = 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [5,1,2,4,3] => [5,1,2,4,3] => ? = 0
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 1
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => ? = 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [5,1,3,2,4] => [5,1,3,2,4] => ? = 1
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [4,1,5,2,3] => [4,1,5,2,3] => ? = 0
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [4,1,3,2,5] => [4,1,3,2,5] => ? = 0
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [5,1,4,3,2] => [5,1,4,3,2] => ? = 0
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 2
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 1
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [5,1,3,4,2] => [5,1,3,4,2] => ? = 0
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 1
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 2
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [5,2,1,3,4] => [5,2,1,3,4] => ? = 2
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [4,5,1,3,2] => [4,5,1,3,2] => ? = 0
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [4,2,1,3,5] => [4,2,1,3,5] => ? = 1
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 0
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [3,4,1,2,5] => [3,4,1,2,5] => ? = 0
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [5,2,1,4,3] => [5,2,1,4,3] => ? = 1
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [3,5,1,4,2] => [3,5,1,4,2] => ? = 0
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 2
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 0
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [5,3,2,1,4] => [5,3,2,1,4] => ? = 1
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [4,5,2,1,3] => [4,5,2,1,3] => ? = 0
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => ? = 0
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => [5,4,2,3,1] => [5,4,2,3,1] => ? = 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => 3
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => 2
{{1,5},{2,3},{4}}
 => [5,3,2,4,1] => [5,3,2,4,1] => [5,3,2,4,1] => ? = 0
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,5,2,4,3] => [1,5,2,4,3] => 2
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 3
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [5,2,3,1,4] => [5,2,3,1,4] => ? = 2
{{1,4},{2,5},{3}}
 => [4,5,3,1,2] => [4,5,3,1,2] => [4,5,3,1,2] => ? = 0
{{1,4},{2},{3,5}}
 => [4,2,5,1,3] => [4,2,5,1,3] => [4,2,5,1,3] => ? = 1
{{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => [4,2,3,1,5] => [4,2,3,1,5] => ? = 0
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => ? = 0
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,5,3,2,4] => [1,5,3,2,4] => 3
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,4,5,2,3] => [1,4,5,2,3] => 2
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 1
{{1,5},{2},{3,4}}
 => [5,2,4,3,1] => [5,2,4,3,1] => [5,2,4,3,1] => ? = 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,5,4,3,2] => [1,5,4,3,2] => 2
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,3,4] => [1,2,5,3,4] => 4
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [5,2,3,4,1] => [5,2,3,4,1] => ? = 0
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,5,3,4,2] => [1,5,3,4,2] => 1
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => [1,2,5,4,3] => 2
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 3
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4,5,6}}
 => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => ? = 0
{{1,2,3,4,5},{6}}
 => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => ? = 0
{{1,2,3,4,6},{5}}
 => [2,3,4,6,5,1] => [6,1,2,3,5,4] => [6,1,2,3,5,4] => ? = 0
{{1,2,3,4},{5,6}}
 => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [4,1,2,3,6,5] => ? = 1
{{1,2,3,4},{5},{6}}
 => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => ? = 0
{{1,2,3,5,6},{4}}
 => [2,3,5,4,6,1] => [6,1,2,4,3,5] => [6,1,2,4,3,5] => ? = 1
{{1,2,3,5},{4,6}}
 => [2,3,5,6,1,4] => [5,1,2,6,3,4] => [5,1,2,6,3,4] => ? = 0
{{1,2,3,5},{4},{6}}
 => [2,3,5,4,1,6] => [5,1,2,4,3,6] => [5,1,2,4,3,6] => ? = 0
{{1,2,3,6},{4,5}}
 => [2,3,6,5,4,1] => [6,1,2,5,4,3] => [6,1,2,5,4,3] => ? = 0
{{1,2,3},{4,5,6}}
 => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [3,1,2,6,4,5] => ? = 2
{{1,2,3},{4,5},{6}}
 => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [3,1,2,5,4,6] => ? = 1
{{1,2,3,6},{4},{5}}
 => [2,3,6,4,5,1] => [6,1,2,4,5,3] => [6,1,2,4,5,3] => ? = 0
{{1,2,3},{4,6},{5}}
 => [2,3,1,6,5,4] => [3,1,2,6,5,4] => [3,1,2,6,5,4] => ? = 1
Description
The number of alignments of type EN of a signed permutation. An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold: * $-i < 0 < -\pi(i) < \pi(j) < j$ * $i \leq\pi(i) < \pi(j) < j$.