Your data matches 15 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000496
(load all 7 compositions to match this statistic)
Mapping
St000496: 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}}
 => 1
{{1},{2,3}}
 => 0
{{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => 0
{{1,2,4},{3}}
 => 1
{{1,2},{3,4}}
 => 0
{{1,2},{3},{4}}
 => 0
{{1,3,4},{2}}
 => 2
{{1,3},{2,4}}
 => 0
{{1,3},{2},{4}}
 => 1
{{1,4},{2,3}}
 => 1
{{1},{2,3,4}}
 => 0
{{1},{2,3},{4}}
 => 0
{{1,4},{2},{3}}
 => 2
{{1},{2,4},{3}}
 => 1
{{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}}
 => 1
{{1},{2,3},{4,5}}
 => 0
{{1},{2,3},{4},{5}}
 => 0
{{1},{2,4,5},{3}}
 => 2
{{1},{2,4},{3,5}}
 => 0
{{1},{2,4},{3},{5}}
 => 1
{{1},{2,5},{3,4}}
 => 1
{{1},{2},{3,4,5}}
 => 0
{{1},{2},{3,4},{5}}
 => 0
{{1},{2,5},{3},{4}}
 => 2
{{1},{2},{3,5},{4}}
 => 1
{{1},{2},{3},{4,5}}
 => 0
{{1},{2},{3},{4},{5}}
 => 0
Description
The rcs statistic of a set partition. Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$. According to [1, Definition 3], a '''rcs''' (right-closer-smaller) of $S$ is given by a pair $i > j$ such that $j = \operatorname{max} B_b$ and $i \in B_a$ for $a < b$.
Matching statistic: St000057
(load all 2 compositions to match this statistic)
Mapping
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
Mp00112: Set partitions —complement⟶ Set partitions
Mp00258: Set partitions —Standard tableau associated to a set partition⟶ Standard tableaux
St000057: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => {{1}}
 => {{1}}
 => [[1]]
 => 0
{{1,2}}
 => {{1,2}}
 => {{1,2}}
 => [[1,2]]
 => 0
{{1},{2}}
 => {{1},{2}}
 => {{1},{2}}
 => [[1],[2]]
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => {{1,2,3}}
 => [[1,2,3]]
 => 0
{{1,2},{3}}
 => {{1,2},{3}}
 => {{1},{2,3}}
 => [[1,3],[2]]
 => 0
{{1,3},{2}}
 => {{1},{2,3}}
 => {{1,2},{3}}
 => [[1,2],[3]]
 => 1
{{1},{2,3}}
 => {{1,3},{2}}
 => {{1,3},{2}}
 => [[1,3],[2]]
 => 0
{{1},{2},{3}}
 => {{1},{2},{3}}
 => {{1},{2},{3}}
 => [[1],[2],[3]]
 => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => {{1,2,3,4}}
 => [[1,2,3,4]]
 => 0
{{1,2,3},{4}}
 => {{1,2,3},{4}}
 => {{1},{2,3,4}}
 => [[1,3,4],[2]]
 => 0
{{1,2,4},{3}}
 => {{1,2},{3,4}}
 => {{1,2},{3,4}}
 => [[1,2],[3,4]]
 => 1
{{1,2},{3,4}}
 => {{1,2,4},{3}}
 => {{1,3,4},{2}}
 => [[1,3,4],[2]]
 => 0
{{1,2},{3},{4}}
 => {{1,2},{3},{4}}
 => {{1},{2},{3,4}}
 => [[1,4],[2],[3]]
 => 0
{{1,3,4},{2}}
 => {{1},{2,3,4}}
 => {{1,2,3},{4}}
 => [[1,2,3],[4]]
 => 2
{{1,3},{2,4}}
 => {{1,4},{2,3}}
 => {{1,4},{2,3}}
 => [[1,3],[2,4]]
 => 0
{{1,3},{2},{4}}
 => {{1},{2,3},{4}}
 => {{1},{2,3},{4}}
 => [[1,3],[2],[4]]
 => 1
{{1,4},{2,3}}
 => {{1,3,4},{2}}
 => {{1,2,4},{3}}
 => [[1,2,4],[3]]
 => 1
{{1},{2,3,4}}
 => {{1,3},{2,4}}
 => {{1,3},{2,4}}
 => [[1,3],[2,4]]
 => 0
{{1},{2,3},{4}}
 => {{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => [[1,4],[2],[3]]
 => 0
{{1,4},{2},{3}}
 => {{1},{2},{3,4}}
 => {{1,2},{3},{4}}
 => [[1,2],[3],[4]]
 => 2
{{1},{2,4},{3}}
 => {{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => [[1,3],[2],[4]]
 => 1
{{1},{2},{3,4}}
 => {{1,4},{2},{3}}
 => {{1,4},{2},{3}}
 => [[1,4],[2],[3]]
 => 0
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => [[1],[2],[3],[4]]
 => 0
{{1},{2,3,4,5}}
 => {{1,3,5},{2,4}}
 => {{1,3,5},{2,4}}
 => [[1,3,5],[2,4]]
 => 0
{{1},{2,3,4},{5}}
 => {{1,3},{2,4},{5}}
 => {{1},{2,4},{3,5}}
 => [[1,4],[2,5],[3]]
 => 0
{{1},{2,3,5},{4}}
 => {{1,3,5},{2},{4}}
 => {{1,3,5},{2},{4}}
 => [[1,3,5],[2],[4]]
 => 1
{{1},{2,3},{4,5}}
 => {{1,3},{2,5},{4}}
 => {{1,4},{2},{3,5}}
 => [[1,4],[2,5],[3]]
 => 0
{{1},{2,3},{4},{5}}
 => {{1,3},{2},{4},{5}}
 => {{1},{2},{3,5},{4}}
 => [[1,5],[2],[3],[4]]
 => 0
{{1},{2,4,5},{3}}
 => {{1},{2,4},{3,5}}
 => {{1,3},{2,4},{5}}
 => [[1,3],[2,4],[5]]
 => 2
{{1},{2,4},{3,5}}
 => {{1,5},{2,4},{3}}
 => {{1,5},{2,4},{3}}
 => [[1,4],[2,5],[3]]
 => 0
{{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => [[1,4],[2],[3],[5]]
 => 1
{{1},{2,5},{3,4}}
 => {{1,4},{2},{3,5}}
 => {{1,3},{2,5},{4}}
 => [[1,3],[2,5],[4]]
 => 1
{{1},{2},{3,4,5}}
 => {{1,4},{2,5},{3}}
 => {{1,4},{2,5},{3}}
 => [[1,4],[2,5],[3]]
 => 0
{{1},{2},{3,4},{5}}
 => {{1,4},{2},{3},{5}}
 => {{1},{2,5},{3},{4}}
 => [[1,5],[2],[3],[4]]
 => 0
{{1},{2,5},{3},{4}}
 => {{1},{2},{3,5},{4}}
 => {{1,3},{2},{4},{5}}
 => [[1,3],[2],[4],[5]]
 => 2
{{1},{2},{3,5},{4}}
 => {{1},{2,5},{3},{4}}
 => {{1,4},{2},{3},{5}}
 => [[1,4],[2],[3],[5]]
 => 1
{{1},{2},{3},{4,5}}
 => {{1,5},{2},{3},{4}}
 => {{1,5},{2},{3},{4}}
 => [[1,5],[2],[3],[4]]
 => 0
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => [[1],[2],[3],[4],[5]]
 => 0
Description
The Shynar inversion number of a standard tableau. Shynar's inversion number is the number of inversion pairs in a standard Young tableau, where an inversion pair is defined as a pair of integers (x,y) such that y > x and y appears strictly southwest of x in the tableau.
Matching statistic: St000358
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000358: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => [1] => 0
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => [3,2,1] => 0
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
 => [3,2,1] => [2,3,1] => [3,1,2] => 1
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [1,3,2] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,3,2,1] => [4,3,2,1] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [3,4,2,1] => [4,3,1,2] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
{{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] => [2,4,3,1] => [4,1,3,2] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [4,1,3,2] => [2,4,3,1] => 0
{{1,3},{2},{4}}
 => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [3,2,4,1] => [4,2,1,3] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,3,4,1] => [4,1,2,3] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,3,4,2] => [1,4,2,3] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,4,3,2] => [1,5,4,3,2] => 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,4,5,3,2] => [1,5,4,2,3] => 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 0
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,3,5,4,2] => [1,5,2,4,3] => 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,5,2,4,3] => [1,3,5,4,2] => 0
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,3,4,2,5] => [1,4,2,3,5] => 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,4,3,5,2] => [1,5,3,2,4] => 1
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 0
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,3,4,5,2] => [1,5,2,3,4] => 2
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,5,3,4] => 1
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
Description
The number of occurrences of the pattern 31-2. See [[Permutations/#Pattern-avoiding_permutations]] for the definition of the pattern $31\!\!-\!\!2$.
Matching statistic: St000359
(load all 2 compositions to match this statistic)
Mapping
Mp00112: Set partitions —complement⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
St000359: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
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] => [3,2,1] => 0
{{1,2},{3}}
 => {{1},{2,3}}
 => [1,3,2] => [1,3,2] => 0
{{1,3},{2}}
 => {{1,3},{2}}
 => [3,2,1] => [2,3,1] => 1
{{1},{2,3}}
 => {{1,2},{3}}
 => [2,1,3] => [2,1,3] => 0
{{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] => [4,3,2,1] => 0
{{1,2,3},{4}}
 => {{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => 0
{{1,2,4},{3}}
 => {{1,3,4},{2}}
 => [3,2,4,1] => [2,4,3,1] => 1
{{1,2},{3,4}}
 => {{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 0
{{1,2},{3},{4}}
 => {{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 0
{{1,3,4},{2}}
 => {{1,2,4},{3}}
 => [2,4,3,1] => [3,4,2,1] => 2
{{1,3},{2,4}}
 => {{1,3},{2,4}}
 => [3,4,1,2] => [4,1,3,2] => 0
{{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => [1,4,3,2] => [1,3,4,2] => 1
{{1,4},{2,3}}
 => {{1,4},{2,3}}
 => [4,3,2,1] => [3,2,4,1] => 1
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => 0
{{1},{2,3},{4}}
 => {{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => 0
{{1,4},{2},{3}}
 => {{1,4},{2},{3}}
 => [4,2,3,1] => [2,3,4,1] => 2
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => [3,2,1,4] => [2,3,1,4] => 1
{{1},{2},{3,4}}
 => {{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 0
{{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}}
 => [2,3,4,1,5] => [4,3,2,1,5] => 0
{{1},{2,3,4},{5}}
 => {{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,3,2,5] => 0
{{1},{2,3,5},{4}}
 => {{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [2,4,3,1,5] => 1
{{1},{2,3},{4,5}}
 => {{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [2,1,4,3,5] => 0
{{1},{2,3},{4},{5}}
 => {{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => 0
{{1},{2,4,5},{3}}
 => {{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [3,4,2,1,5] => 2
{{1},{2,4},{3,5}}
 => {{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [4,1,3,2,5] => 0
{{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,3,4,2,5] => 1
{{1},{2,5},{3,4}}
 => {{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [3,2,4,1,5] => 1
{{1},{2},{3,4,5}}
 => {{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [3,2,1,4,5] => 0
{{1},{2},{3,4},{5}}
 => {{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => 0
{{1},{2,5},{3},{4}}
 => {{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => [2,3,4,1,5] => 2
{{1},{2},{3,5},{4}}
 => {{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [2,3,1,4,5] => 1
{{1},{2},{3},{4,5}}
 => {{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [2,1,3,4,5] => 0
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => 0
Description
The number of occurrences of the pattern 23-1. See [[Permutations/#Pattern-avoiding_permutations]] for the definition of the pattern $23\!\!-\!\!1$.
Matching statistic: St001683
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St001683: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => [1] => 0
{{1,2}}
 => [2,1] => [2,1] => [1,2] => 0
{{1},{2}}
 => [1,2] => [1,2] => [2,1] => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => [1,2,3] => 0
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [3,1,2] => 0
{{1,3},{2}}
 => [3,2,1] => [2,3,1] => [1,3,2] => 1
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [2,3,1] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [3,2,1] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,3,2,1] => [1,2,3,4] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => [4,1,2,3] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [3,4,2,1] => [1,2,4,3] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [3,4,1,2] => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [4,3,1,2] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [2,4,3,1] => [1,3,4,2] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [4,1,3,2] => [2,3,1,4] => 0
{{1,3},{2},{4}}
 => [3,2,1,4] => [2,3,1,4] => [4,1,3,2] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [3,2,4,1] => [1,4,2,3] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => [2,3,4,1] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [4,2,3,1] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,3,4,1] => [1,4,3,2] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,3,4,2] => [2,4,3,1] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [3,4,2,1] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,4,3,2] => [2,3,4,5,1] => 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,3,2,5] => [5,2,3,4,1] => 0
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,4,5,3,2] => [2,3,5,4,1] => 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => [4,5,2,3,1] => 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => [5,4,2,3,1] => 0
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,3,5,4,2] => [2,4,5,3,1] => 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,5,2,4,3] => [3,4,2,5,1] => 0
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,3,4,2,5] => [5,2,4,3,1] => 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,4,3,5,2] => [2,5,3,4,1] => 1
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,4,3] => [3,4,5,2,1] => 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => [5,3,4,2,1] => 0
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,3,4,5,2] => [2,5,4,3,1] => 2
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,4,5,3] => [3,5,4,2,1] => 1
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => [4,5,3,2,1] => 0
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => 0
Description
The number of distinct positions of the pattern letter 3 in occurrences of 132 in a permutation.
Matching statistic: St001882
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001882: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => [1] => 0
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => [3,2,1] => 0
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 0
{{1,3},{2}}
 => [3,2,1] => [2,3,1] => [2,3,1] => 1
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [1,3,2] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,3,2,1] => [4,3,2,1] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => [3,2,1,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [3,4,2,1] => [3,4,2,1] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
{{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] => [2,4,3,1] => [2,4,3,1] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [4,1,3,2] => [4,1,3,2] => 0
{{1,3},{2},{4}}
 => [3,2,1,4] => [2,3,1,4] => [2,3,1,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [3,2,4,1] => [3,2,4,1] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => [1,4,3,2] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,3,4,1] => [2,3,4,1] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,3,4,2] => [1,3,4,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,4,3,2] => [1,5,4,3,2] => 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,3,2,5] => [1,4,3,2,5] => 0
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,4,5,3,2] => [1,4,5,3,2] => 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 0
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,3,5,4,2] => [1,3,5,4,2] => 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,5,2,4,3] => [1,5,2,4,3] => 0
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,4,3,5,2] => [1,4,3,5,2] => 1
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,5,4,3] => 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 0
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,3,4,5,2] => [1,3,4,5,2] => 2
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,4,5,3] => 1
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 0
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
Description
The number of occurrences of a type-B 231 pattern in a signed permutation. For a signed permutation $\pi\in\mathfrak H_n$, a triple $-n \leq i < j < k\leq n$ is an occurrence of the type-B $231$ pattern, if $1 \leq j < k$, $\pi(i) < \pi(j)$ and $\pi(i)$ is one larger than $\pi(k)$, i.e., $\pi(i) = \pi(k) + 1$ if $\pi(k) \neq -1$ and $\pi(i) = 1$ otherwise.
Matching statistic: St000589
(load all 6 compositions to match this statistic)
Mapping
Mp00174: Set partitions —dual major index to intertwining number⟶ Set partitions
St000589: Set partitions ⟶ ℤResult quality: 97% ●values known / values provided: 97%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => {{1}}
 => ? = 0
{{1,2}}
 => {{1,2}}
 => 0
{{1},{2}}
 => {{1},{2}}
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => 0
{{1,2},{3}}
 => {{1,2},{3}}
 => 0
{{1,3},{2}}
 => {{1},{2,3}}
 => 1
{{1},{2,3}}
 => {{1,3},{2}}
 => 0
{{1},{2},{3}}
 => {{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => {{1,2,3},{4}}
 => 0
{{1,2,4},{3}}
 => {{1,2},{3,4}}
 => 1
{{1,2},{3,4}}
 => {{1,2,4},{3}}
 => 0
{{1,2},{3},{4}}
 => {{1,2},{3},{4}}
 => 0
{{1,3,4},{2}}
 => {{1},{2,3,4}}
 => 2
{{1,3},{2,4}}
 => {{1,4},{2,3}}
 => 0
{{1,3},{2},{4}}
 => {{1},{2,3},{4}}
 => 1
{{1,4},{2,3}}
 => {{1,3,4},{2}}
 => 1
{{1},{2,3,4}}
 => {{1,3},{2,4}}
 => 0
{{1},{2,3},{4}}
 => {{1,3},{2},{4}}
 => 0
{{1,4},{2},{3}}
 => {{1},{2},{3,4}}
 => 2
{{1},{2,4},{3}}
 => {{1},{2,4},{3}}
 => 1
{{1},{2},{3,4}}
 => {{1,4},{2},{3}}
 => 0
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => 0
{{1},{2,3,4,5}}
 => {{1,3,5},{2,4}}
 => 0
{{1},{2,3,4},{5}}
 => {{1,3},{2,4},{5}}
 => 0
{{1},{2,3,5},{4}}
 => {{1,3,5},{2},{4}}
 => 1
{{1},{2,3},{4,5}}
 => {{1,3},{2,5},{4}}
 => 0
{{1},{2,3},{4},{5}}
 => {{1,3},{2},{4},{5}}
 => 0
{{1},{2,4,5},{3}}
 => {{1},{2,4},{3,5}}
 => 2
{{1},{2,4},{3,5}}
 => {{1,5},{2,4},{3}}
 => 0
{{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => 1
{{1},{2,5},{3,4}}
 => {{1,4},{2},{3,5}}
 => 1
{{1},{2},{3,4,5}}
 => {{1,4},{2,5},{3}}
 => 0
{{1},{2},{3,4},{5}}
 => {{1,4},{2},{3},{5}}
 => 0
{{1},{2,5},{3},{4}}
 => {{1},{2},{3,5},{4}}
 => 2
{{1},{2},{3,5},{4}}
 => {{1},{2,5},{3},{4}}
 => 1
{{1},{2},{3},{4,5}}
 => {{1,5},{2},{3},{4}}
 => 0
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{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: St000607
(load all 3 compositions to match this statistic)
Mapping
Mp00112: Set partitions —complement⟶ Set partitions
Mp00171: Set partitions —intertwining number to dual major index⟶ Set partitions
St000607: Set partitions ⟶ ℤResult quality: 97% ●values known / values provided: 97%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => {{1}}
 => {{1}}
 => ? = 0
{{1,2}}
 => {{1,2}}
 => {{1,2}}
 => 0
{{1},{2}}
 => {{1},{2}}
 => {{1},{2}}
 => 0
{{1,2,3}}
 => {{1,2,3}}
 => {{1,2,3}}
 => 0
{{1,2},{3}}
 => {{1},{2,3}}
 => {{1,3},{2}}
 => 0
{{1,3},{2}}
 => {{1,3},{2}}
 => {{1},{2,3}}
 => 1
{{1},{2,3}}
 => {{1,2},{3}}
 => {{1,2},{3}}
 => 0
{{1},{2},{3}}
 => {{1},{2},{3}}
 => {{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => {{1,2,3,4}}
 => {{1,2,3,4}}
 => 0
{{1,2,3},{4}}
 => {{1},{2,3,4}}
 => {{1,3,4},{2}}
 => 0
{{1,2,4},{3}}
 => {{1,3,4},{2}}
 => {{1,4},{2,3}}
 => 1
{{1,2},{3,4}}
 => {{1,2},{3,4}}
 => {{1,2,4},{3}}
 => 0
{{1,2},{3},{4}}
 => {{1},{2},{3,4}}
 => {{1,4},{2},{3}}
 => 0
{{1,3,4},{2}}
 => {{1,2,4},{3}}
 => {{1,2},{3,4}}
 => 2
{{1,3},{2,4}}
 => {{1,3},{2,4}}
 => {{1},{2,3,4}}
 => 0
{{1,3},{2},{4}}
 => {{1},{2,4},{3}}
 => {{1},{2,4},{3}}
 => 1
{{1,4},{2,3}}
 => {{1,4},{2,3}}
 => {{1,3},{2,4}}
 => 1
{{1},{2,3,4}}
 => {{1,2,3},{4}}
 => {{1,2,3},{4}}
 => 0
{{1},{2,3},{4}}
 => {{1},{2,3},{4}}
 => {{1,3},{2},{4}}
 => 0
{{1,4},{2},{3}}
 => {{1,4},{2},{3}}
 => {{1},{2},{3,4}}
 => 2
{{1},{2,4},{3}}
 => {{1,3},{2},{4}}
 => {{1},{2,3},{4}}
 => 1
{{1},{2},{3,4}}
 => {{1,2},{3},{4}}
 => {{1,2},{3},{4}}
 => 0
{{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => {{1},{2},{3},{4}}
 => 0
{{1},{2,3,4,5}}
 => {{1,2,3,4},{5}}
 => {{1,2,3,4},{5}}
 => 0
{{1},{2,3,4},{5}}
 => {{1},{2,3,4},{5}}
 => {{1,3,4},{2},{5}}
 => 0
{{1},{2,3,5},{4}}
 => {{1,3,4},{2},{5}}
 => {{1,4},{2,3},{5}}
 => 1
{{1},{2,3},{4,5}}
 => {{1,2},{3,4},{5}}
 => {{1,2,4},{3},{5}}
 => 0
{{1},{2,3},{4},{5}}
 => {{1},{2},{3,4},{5}}
 => {{1,4},{2},{3},{5}}
 => 0
{{1},{2,4,5},{3}}
 => {{1,2,4},{3},{5}}
 => {{1,2},{3,4},{5}}
 => 2
{{1},{2,4},{3,5}}
 => {{1,3},{2,4},{5}}
 => {{1},{2,3,4},{5}}
 => 0
{{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => {{1},{2,4},{3},{5}}
 => 1
{{1},{2,5},{3,4}}
 => {{1,4},{2,3},{5}}
 => {{1,3},{2,4},{5}}
 => 1
{{1},{2},{3,4,5}}
 => {{1,2,3},{4},{5}}
 => {{1,2,3},{4},{5}}
 => 0
{{1},{2},{3,4},{5}}
 => {{1},{2,3},{4},{5}}
 => {{1,3},{2},{4},{5}}
 => 0
{{1},{2,5},{3},{4}}
 => {{1,4},{2},{3},{5}}
 => {{1},{2},{3,4},{5}}
 => 2
{{1},{2},{3,5},{4}}
 => {{1,3},{2},{4},{5}}
 => {{1},{2,3},{4},{5}}
 => 1
{{1},{2},{3},{4,5}}
 => {{1,2},{3},{4},{5}}
 => {{1,2},{3},{4},{5}}
 => 0
{{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => {{1},{2},{3},{4},{5}}
 => 0
Description
The number of occurrences of the pattern {{1},{2,3}} such that 2 is minimal, 3 is maximal, (2,3) are consecutive in a block.
Matching statistic: St001771
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00194: Signed permutations —Foata-Han inverse⟶ Signed permutations
St001771: Signed permutations ⟶ ℤResult quality: 63% ●values known / values provided: 63%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => [1] => 0
{{1,2}}
 => [2,1] => [2,1] => [-2,1] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [2,3,1] => [-3,-2,1] => 0
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [-2,1,3] => 0
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [2,-3,1] => 1
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [-3,1,2] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [2,3,4,1] => [-4,-3,-2,1] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [2,3,1,4] => [-3,-2,1,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [2,4,3,1] => [3,-4,-2,1] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [-4,-2,1,3] => 0
{{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] => [3,2,4,1] => [2,-4,-3,1] => 2
{{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] => [2,-3,1,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [-3,2,-4,1] => 1
{{1},{2,3,4}}
 => [1,3,4,2] => [1,3,4,2] => [-4,-3,1,2] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [-3,1,2,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => [2,3,-4,1] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => [3,-4,1,2] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [-4,1,2,3] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,3,4,5,2] => [-5,-4,-3,1,2] => ? = 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,3,4,2,5] => [-4,-3,1,2,5] => ? = 0
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,3,5,4,2] => [4,-5,-3,1,2] => ? = 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => [-5,-3,1,2,4] => ? = 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => [-3,1,2,4,5] => ? = 0
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,4,3,5,2] => [3,-5,-4,1,2] => ? = 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,4,5,2,3] => [4,5,1,2,3] => ? = 0
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => [3,-4,1,2,5] => ? = 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,5,4,3,2] => [-4,3,-5,1,2] => ? = 1
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,4,5,3] => [-5,-4,1,2,3] => ? = 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => [-4,1,2,3,5] => ? = 0
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,5,3,4,2] => [3,4,-5,1,2] => ? = 2
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => [4,-5,1,2,3] => ? = 1
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => [-5,1,2,3,4] => ? = 0
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
Description
The number of occurrences of the signed pattern 1-2 in a signed permutation. This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < -\pi(j)$.
Matching statistic: St001604
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00204: Permutations —LLPS⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 33%
Values
{{1}}
 => [1] => [1]
 => []
 => ? = 0
{{1,2}}
 => [2,1] => [2]
 => []
 => ? = 0
{{1},{2}}
 => [1,2] => [1,1]
 => [1]
 => ? = 0
{{1,2,3}}
 => [2,3,1] => [2,1]
 => [1]
 => ? = 0
{{1,2},{3}}
 => [2,1,3] => [2,1]
 => [1]
 => ? = 0
{{1,3},{2}}
 => [3,2,1] => [3]
 => []
 => ? = 1
{{1},{2,3}}
 => [1,3,2] => [2,1]
 => [1]
 => ? = 0
{{1},{2},{3}}
 => [1,2,3] => [1,1,1]
 => [1,1]
 => ? = 0
{{1,2,3,4}}
 => [2,3,4,1] => [2,1,1]
 => [1,1]
 => ? = 0
{{1,2,3},{4}}
 => [2,3,1,4] => [2,1,1]
 => [1,1]
 => ? = 0
{{1,2,4},{3}}
 => [2,4,3,1] => [3,1]
 => [1]
 => ? = 1
{{1,2},{3,4}}
 => [2,1,4,3] => [2,2]
 => [2]
 => ? = 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,1]
 => [1,1]
 => ? = 0
{{1,3,4},{2}}
 => [3,2,4,1] => [3,1]
 => [1]
 => ? = 2
{{1,3},{2,4}}
 => [3,4,1,2] => [2,1,1]
 => [1,1]
 => ? = 0
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,1]
 => [1]
 => ? = 1
{{1,4},{2,3}}
 => [4,3,2,1] => [4]
 => []
 => ? = 1
{{1},{2,3,4}}
 => [1,3,4,2] => [2,1,1]
 => [1,1]
 => ? = 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [2,1,1]
 => [1,1]
 => ? = 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [3,1]
 => [1]
 => ? = 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [3,1]
 => [1]
 => ? = 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [2,1,1]
 => [1,1]
 => ? = 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,1,1,1]
 => [1,1,1]
 => 0
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [2,1,1,1]
 => [1,1,1]
 => 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [2,1,1,1]
 => [1,1,1]
 => 0
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [3,1,1]
 => [1,1]
 => ? = 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [2,2,1]
 => [2,1]
 => 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [2,1,1,1]
 => [1,1,1]
 => 0
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [3,1,1]
 => [1,1]
 => ? = 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [2,1,1,1]
 => [1,1,1]
 => 0
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [3,1,1]
 => [1,1]
 => ? = 1
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [4,1]
 => [1]
 => ? = 1
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [2,1,1,1]
 => [1,1,1]
 => 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [2,1,1,1]
 => [1,1,1]
 => 0
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [3,1,1]
 => [1,1]
 => ? = 2
{{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [3,1,1]
 => [1,1]
 => ? = 1
{{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [2,1,1,1]
 => [1,1,1]
 => 0
{{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,1,1,1,1]
 => [1,1,1,1]
 => 0
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
The following 5 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001857The number of edges in the reduced word graph of a signed permutation. St000102The charge of a semistandard tableau. St001964The interval resolution global dimension of a poset. St000181The number of connected components of the Hasse diagram for the poset. St001890The maximum magnitude of the Möbius function of a poset.