Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001687
(load all 2 compositions to match this statistic)
Mapping
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
St001687: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1]
 => [1]
 => [1,0,1,0]
 => [2,1] => 0
[2,1]
 => [1]
 => [1,0,1,0]
 => [2,1] => 0
[1,1,1]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1
[3,1]
 => [1]
 => [1,0,1,0]
 => [2,1] => 0
[2,2]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 0
[2,1,1]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1
[1,1,1,1]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 1
[4,1]
 => [1]
 => [1,0,1,0]
 => [2,1] => 0
[3,2]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 0
[3,1,1]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1
[2,2,1]
 => [2,1]
 => [1,0,1,0,1,0]
 => [2,3,1] => 0
[2,1,1,1]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 1
[1,1,1,1,1]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => 1
[5,1]
 => [1]
 => [1,0,1,0]
 => [2,1] => 0
[4,2]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 0
[4,1,1]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1
[3,3]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,2,4,3] => 0
[3,2,1]
 => [2,1]
 => [1,0,1,0,1,0]
 => [2,3,1] => 0
[3,1,1,1]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 1
[2,2,2]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 1
[2,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [2,4,1,3] => 1
[2,1,1,1,1]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => 1
[1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,3,4,5,6] => 1
[6,1]
 => [1]
 => [1,0,1,0]
 => [2,1] => 0
[5,2]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 0
[5,1,1]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1
[4,3]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,2,4,3] => 0
[4,2,1]
 => [2,1]
 => [1,0,1,0,1,0]
 => [2,3,1] => 0
[4,1,1,1]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 1
[3,3,1]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [3,1,4,2] => 1
[3,2,2]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 1
[3,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [2,4,1,3] => 1
[3,1,1,1,1]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => 1
[2,2,2,1]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [2,3,1,4] => 2
[2,2,1,1,1]
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [2,5,1,3,4] => 1
[2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [2,1,3,4,5,6] => 1
[7,1]
 => [1]
 => [1,0,1,0]
 => [2,1] => 0
[6,2]
 => [2]
 => [1,1,0,0,1,0]
 => [1,3,2] => 0
[6,1,1]
 => [1,1]
 => [1,0,1,1,0,0]
 => [2,1,3] => 1
[5,3]
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [1,2,4,3] => 0
[5,2,1]
 => [2,1]
 => [1,0,1,0,1,0]
 => [2,3,1] => 0
[5,1,1,1]
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [2,1,3,4] => 1
[4,4]
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,2,3,5,4] => 0
[4,3,1]
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [3,1,4,2] => 1
[4,2,2]
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [1,3,2,4] => 1
[4,2,1,1]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [2,4,1,3] => 1
[4,1,1,1,1]
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [2,1,3,4,5] => 1
[3,3,2]
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [1,3,4,2] => 0
[3,3,1,1]
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [2,1,4,3] => 1
[3,2,2,1]
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [2,3,1,4] => 2
Description
The number of distinct positions of the pattern letter 2 in occurrences of 213 in a permutation.
Matching statistic: St000461
Mapping
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
St000461: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 40%
Values
[1,1]
 => [[1],[2]]
 => [2,1] => [2,1] => 0
[2,1]
 => [[1,2],[3]]
 => [3,1,2] => [3,1,2] => 0
[1,1,1]
 => [[1],[2],[3]]
 => [3,2,1] => [2,3,1] => 1
[3,1]
 => [[1,2,3],[4]]
 => [4,1,2,3] => [4,1,2,3] => 0
[2,2]
 => [[1,2],[3,4]]
 => [3,4,1,2] => [4,1,3,2] => 0
[2,1,1]
 => [[1,2],[3],[4]]
 => [4,3,1,2] => [3,1,4,2] => 1
[1,1,1,1]
 => [[1],[2],[3],[4]]
 => [4,3,2,1] => [2,3,4,1] => 1
[4,1]
 => [[1,2,3,4],[5]]
 => [5,1,2,3,4] => [5,1,2,3,4] => 0
[3,2]
 => [[1,2,3],[4,5]]
 => [4,5,1,2,3] => [5,1,2,4,3] => 0
[3,1,1]
 => [[1,2,3],[4],[5]]
 => [5,4,1,2,3] => [4,1,2,5,3] => 1
[2,2,1]
 => [[1,2],[3,4],[5]]
 => [5,3,4,1,2] => [4,1,5,3,2] => 0
[2,1,1,1]
 => [[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => [3,1,4,5,2] => 1
[1,1,1,1,1]
 => [[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => [2,3,4,5,1] => 1
[5,1]
 => [[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 0
[4,2]
 => [[1,2,3,4],[5,6]]
 => [5,6,1,2,3,4] => [6,1,2,3,5,4] => 0
[4,1,1]
 => [[1,2,3,4],[5],[6]]
 => [6,5,1,2,3,4] => [5,1,2,3,6,4] => 1
[3,3]
 => [[1,2,3],[4,5,6]]
 => [4,5,6,1,2,3] => [6,1,2,4,5,3] => 0
[3,2,1]
 => [[1,2,3],[4,5],[6]]
 => [6,4,5,1,2,3] => [5,1,2,6,4,3] => 0
[3,1,1,1]
 => [[1,2,3],[4],[5],[6]]
 => [6,5,4,1,2,3] => [4,1,2,5,6,3] => 1
[2,2,2]
 => [[1,2],[3,4],[5,6]]
 => [5,6,3,4,1,2] => [4,1,6,3,5,2] => 1
[2,2,1,1]
 => [[1,2],[3,4],[5],[6]]
 => [6,5,3,4,1,2] => [4,1,5,3,6,2] => 1
[2,1,1,1,1]
 => [[1,2],[3],[4],[5],[6]]
 => [6,5,4,3,1,2] => [3,1,4,5,6,2] => 1
[1,1,1,1,1,1]
 => [[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => [2,3,4,5,6,1] => 1
[6,1]
 => [[1,2,3,4,5,6],[7]]
 => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => ? = 0
[5,2]
 => [[1,2,3,4,5],[6,7]]
 => [6,7,1,2,3,4,5] => [7,1,2,3,4,6,5] => ? = 0
[5,1,1]
 => [[1,2,3,4,5],[6],[7]]
 => [7,6,1,2,3,4,5] => [6,1,2,3,4,7,5] => ? = 1
[4,3]
 => [[1,2,3,4],[5,6,7]]
 => [5,6,7,1,2,3,4] => [7,1,2,3,5,6,4] => ? = 0
[4,2,1]
 => [[1,2,3,4],[5,6],[7]]
 => [7,5,6,1,2,3,4] => [6,1,2,3,7,5,4] => ? = 0
[4,1,1,1]
 => [[1,2,3,4],[5],[6],[7]]
 => [7,6,5,1,2,3,4] => [5,1,2,3,6,7,4] => ? = 1
[3,3,1]
 => [[1,2,3],[4,5,6],[7]]
 => [7,4,5,6,1,2,3] => [6,1,2,7,4,5,3] => ? = 1
[3,2,2]
 => [[1,2,3],[4,5],[6,7]]
 => [6,7,4,5,1,2,3] => [5,1,2,7,4,6,3] => ? = 1
[3,2,1,1]
 => [[1,2,3],[4,5],[6],[7]]
 => [7,6,4,5,1,2,3] => [5,1,2,6,4,7,3] => ? = 1
[3,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7]]
 => [7,6,5,4,1,2,3] => [4,1,2,5,6,7,3] => ? = 1
[2,2,2,1]
 => [[1,2],[3,4],[5,6],[7]]
 => [7,5,6,3,4,1,2] => [4,1,6,3,7,5,2] => ? = 2
[2,2,1,1,1]
 => [[1,2],[3,4],[5],[6],[7]]
 => [7,6,5,3,4,1,2] => [4,1,5,3,6,7,2] => ? = 1
[2,1,1,1,1,1]
 => [[1,2],[3],[4],[5],[6],[7]]
 => [7,6,5,4,3,1,2] => [3,1,4,5,6,7,2] => ? = 1
[7,1]
 => [[1,2,3,4,5,6,7],[8]]
 => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => ? = 0
[6,2]
 => [[1,2,3,4,5,6],[7,8]]
 => [7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,7,6] => ? = 0
[6,1,1]
 => [[1,2,3,4,5,6],[7],[8]]
 => [8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,6] => ? = 1
[5,3]
 => [[1,2,3,4,5],[6,7,8]]
 => [6,7,8,1,2,3,4,5] => [8,1,2,3,4,6,7,5] => ? = 0
[5,2,1]
 => [[1,2,3,4,5],[6,7],[8]]
 => [8,6,7,1,2,3,4,5] => [7,1,2,3,4,8,6,5] => ? = 0
[5,1,1,1]
 => [[1,2,3,4,5],[6],[7],[8]]
 => [8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,5] => ? = 1
[4,4]
 => [[1,2,3,4],[5,6,7,8]]
 => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => ? = 0
[4,3,1]
 => [[1,2,3,4],[5,6,7],[8]]
 => [8,5,6,7,1,2,3,4] => [7,1,2,3,8,5,6,4] => ? = 1
[4,2,2]
 => [[1,2,3,4],[5,6],[7,8]]
 => [7,8,5,6,1,2,3,4] => [6,1,2,3,8,5,7,4] => ? = 1
[4,2,1,1]
 => [[1,2,3,4],[5,6],[7],[8]]
 => [8,7,5,6,1,2,3,4] => [6,1,2,3,7,5,8,4] => ? = 1
[4,1,1,1,1]
 => [[1,2,3,4],[5],[6],[7],[8]]
 => [8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,4] => ? = 1
[3,3,2]
 => [[1,2,3],[4,5,6],[7,8]]
 => [7,8,4,5,6,1,2,3] => [6,1,2,8,4,5,7,3] => ? = 0
[3,3,1,1]
 => [[1,2,3],[4,5,6],[7],[8]]
 => [8,7,4,5,6,1,2,3] => [6,1,2,7,4,5,8,3] => ? = 1
[3,2,2,1]
 => [[1,2,3],[4,5],[6,7],[8]]
 => [8,6,7,4,5,1,2,3] => [5,1,2,7,4,8,6,3] => ? = 2
[3,2,1,1,1]
 => [[1,2,3],[4,5],[6],[7],[8]]
 => [8,7,6,4,5,1,2,3] => [5,1,2,6,4,7,8,3] => ? = 1
[3,1,1,1,1,1]
 => [[1,2,3],[4],[5],[6],[7],[8]]
 => [8,7,6,5,4,1,2,3] => [4,1,2,5,6,7,8,3] => ? = 1
[2,2,2,2]
 => [[1,2],[3,4],[5,6],[7,8]]
 => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => ? = 1
[2,2,2,1,1]
 => [[1,2],[3,4],[5,6],[7],[8]]
 => [8,7,5,6,3,4,1,2] => [4,1,6,3,7,5,8,2] => ? = 2
[2,2,1,1,1,1]
 => [[1,2],[3,4],[5],[6],[7],[8]]
 => [8,7,6,5,3,4,1,2] => [4,1,5,3,6,7,8,2] => ? = 1
[8,1]
 => [[1,2,3,4,5,6,7,8],[9]]
 => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => ? = 0
[7,2]
 => [[1,2,3,4,5,6,7],[8,9]]
 => [8,9,1,2,3,4,5,6,7] => [9,1,2,3,4,5,6,8,7] => ? = 0
[7,1,1]
 => [[1,2,3,4,5,6,7],[8],[9]]
 => [9,8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,9,7] => ? = 1
[6,3]
 => [[1,2,3,4,5,6],[7,8,9]]
 => [7,8,9,1,2,3,4,5,6] => [9,1,2,3,4,5,7,8,6] => ? = 0
[6,2,1]
 => [[1,2,3,4,5,6],[7,8],[9]]
 => [9,7,8,1,2,3,4,5,6] => [8,1,2,3,4,5,9,7,6] => ? = 0
[6,1,1,1]
 => [[1,2,3,4,5,6],[7],[8],[9]]
 => [9,8,7,1,2,3,4,5,6] => [7,1,2,3,4,5,8,9,6] => ? = 1
[5,4]
 => [[1,2,3,4,5],[6,7,8,9]]
 => [6,7,8,9,1,2,3,4,5] => [9,1,2,3,4,6,7,8,5] => ? = 0
[5,3,1]
 => [[1,2,3,4,5],[6,7,8],[9]]
 => [9,6,7,8,1,2,3,4,5] => [8,1,2,3,4,9,6,7,5] => ? = 1
[5,2,2]
 => [[1,2,3,4,5],[6,7],[8,9]]
 => [8,9,6,7,1,2,3,4,5] => [7,1,2,3,4,9,6,8,5] => ? = 1
[5,2,1,1]
 => [[1,2,3,4,5],[6,7],[8],[9]]
 => [9,8,6,7,1,2,3,4,5] => [7,1,2,3,4,8,6,9,5] => ? = 1
[5,1,1,1,1]
 => [[1,2,3,4,5],[6],[7],[8],[9]]
 => [9,8,7,6,1,2,3,4,5] => [6,1,2,3,4,7,8,9,5] => ? = 1
[4,4,1]
 => [[1,2,3,4],[5,6,7,8],[9]]
 => [9,5,6,7,8,1,2,3,4] => [8,1,2,3,9,5,6,7,4] => ? = 1
[4,3,2]
 => [[1,2,3,4],[5,6,7],[8,9]]
 => [8,9,5,6,7,1,2,3,4] => [7,1,2,3,9,5,6,8,4] => ? = 0
[4,3,1,1]
 => [[1,2,3,4],[5,6,7],[8],[9]]
 => [9,8,5,6,7,1,2,3,4] => [7,1,2,3,8,5,6,9,4] => ? = 1
[4,2,2,1]
 => [[1,2,3,4],[5,6],[7,8],[9]]
 => [9,7,8,5,6,1,2,3,4] => [6,1,2,3,8,5,9,7,4] => ? = 2
[4,2,1,1,1]
 => [[1,2,3,4],[5,6],[7],[8],[9]]
 => [9,8,7,5,6,1,2,3,4] => [6,1,2,3,7,5,8,9,4] => ? = 1
[4,1,1,1,1,1]
 => [[1,2,3,4],[5],[6],[7],[8],[9]]
 => [9,8,7,6,5,1,2,3,4] => [5,1,2,3,6,7,8,9,4] => ? = 1
[3,3,3]
 => [[1,2,3],[4,5,6],[7,8,9]]
 => [7,8,9,4,5,6,1,2,3] => [6,1,2,9,4,5,7,8,3] => ? = 1
Description
The rix statistic of a permutation. This statistic is defined recursively as follows: $rix([]) = 0$, and if $w_i = \max\{w_1, w_2,\dots, w_k\}$, then $rix(w) := 0$ if $i = 1 < k$, $rix(w) := 1 + rix(w_1,w_2,\dots,w_{k−1})$ if $i = k$ and $rix(w) := rix(w_{i+1},w_{i+2},\dots,w_k)$ if $1 < i < k$.