Processing math: 100%

Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001687
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001687: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => 0
{{1,2}}
 => [2,1] => [1,2] => 0
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => 0
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => 0
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => 0
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => 0
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => 0
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => 0
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => 0
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => 0
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => 0
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => 0
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => 1
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => 0
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => 0
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => 0
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => 0
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => 2
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => 2
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => 1
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => 1
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => 1
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => 1
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => 1
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => 1
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => 0
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => 1
Description
The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation.
Matching statistic: St000562
(load all 2 compositions to match this statistic)
Mapping
St000562: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => ? = 0
{{1,2}}
 => 0
{{1},{2}}
 => 0
{{1,2,3}}
 => 0
{{1,2},{3}}
 => 0
{{1,3},{2}}
 => 0
{{1},{2,3}}
 => 0
{{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => 0
{{1,2,4},{3}}
 => 0
{{1,2},{3,4}}
 => 0
{{1,2},{3},{4}}
 => 0
{{1,3,4},{2}}
 => 0
{{1,3},{2,4}}
 => 1
{{1,3},{2},{4}}
 => 1
{{1,4},{2,3}}
 => 0
{{1},{2,3,4}}
 => 0
{{1},{2,3},{4}}
 => 0
{{1,4},{2},{3}}
 => 0
{{1},{2,4},{3}}
 => 0
{{1},{2},{3,4}}
 => 0
{{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}}
 => 0
{{1,2,3},{4},{5}}
 => 0
{{1,2,4,5},{3}}
 => 0
{{1,2,4},{3,5}}
 => 1
{{1,2,4},{3},{5}}
 => 1
{{1,2,5},{3,4}}
 => 0
{{1,2},{3,4,5}}
 => 0
{{1,2},{3,4},{5}}
 => 0
{{1,2,5},{3},{4}}
 => 0
{{1,2},{3,5},{4}}
 => 0
{{1,2},{3},{4,5}}
 => 0
{{1,2},{3},{4},{5}}
 => 0
{{1,3,4,5},{2}}
 => 0
{{1,3,4},{2,5}}
 => 2
{{1,3,4},{2},{5}}
 => 2
{{1,3,5},{2,4}}
 => 1
{{1,3},{2,4,5}}
 => 1
{{1,3},{2,4},{5}}
 => 1
{{1,3,5},{2},{4}}
 => 1
{{1,3},{2,5},{4}}
 => 1
{{1,3},{2},{4,5}}
 => 1
{{1,3},{2},{4},{5}}
 => 1
{{1,4,5},{2,3}}
 => 0
{{1,4},{2,3,5}}
 => 1
{{1,4},{2,3},{5}}
 => 1
Description
The number of internal points of a set partition. An element e is internal, if there are f<e<g such that the blocks of f and g have larger minimal element than the block of e. See Section 5.5 of [1]