- FindStat

Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000342
(load all 4 compositions to match this statistic)

Mapping

St000342: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1] => 1
[1,2] => 5
[2,1] => 4
[1,2,3] => 14
[1,3,2] => 13
[2,1,3] => 13
[2,3,1] => 11
[3,1,2] => 11
[3,2,1] => 10
[1,2,3,4] => 30
[1,2,4,3] => 29
[1,3,2,4] => 29
[1,3,4,2] => 27
[1,4,2,3] => 27
[1,4,3,2] => 26
[2,1,3,4] => 29
[2,1,4,3] => 28
[2,3,1,4] => 27
[2,3,4,1] => 24
[2,4,1,3] => 25
[2,4,3,1] => 23
[3,1,2,4] => 27
[3,1,4,2] => 25
[3,2,1,4] => 26
[3,2,4,1] => 23
[3,4,1,2] => 22
[3,4,2,1] => 21
[4,1,2,3] => 24
[4,1,3,2] => 23
[4,2,1,3] => 23
[4,2,3,1] => 21
[4,3,1,2] => 21
[4,3,2,1] => 20
[1,2,3,4,5] => 55
[1,2,3,5,4] => 54
[1,2,4,3,5] => 54
[1,2,4,5,3] => 52
[1,2,5,3,4] => 52
[1,2,5,4,3] => 51
[1,3,2,4,5] => 54
[1,3,2,5,4] => 53
[1,3,4,2,5] => 52
[1,3,4,5,2] => 49
[1,3,5,2,4] => 50
[1,3,5,4,2] => 48
[1,4,2,3,5] => 52
[1,4,2,5,3] => 50
[1,4,3,2,5] => 51
[1,4,3,5,2] => 48
[1,4,5,2,3] => 47

Description

The cosine of a permutation. For a permutation

$\pi = [\pi_1,\ldots,\pi_n]$ , this is given by

$\sum_{i=1}^n (i\pi_i)$ . The name comes from the observation that this equals

$\frac{n(n+1)(2n+1)}{6}\cos(\theta)$ where

$\theta$ is the angle between the vector

$(\pi_1,\ldots,\pi_n)$ and the vector

$(1,\ldots,n)$ , see [1].

Matching statistic: St000114

Mapping

Mp00063: Permutations —to alternating sign matrix⟶ Alternating sign matrices
Mp00001: Alternating sign matrices —to semistandard tableau via monotone triangles⟶ Semistandard tableaux
Mp00076: Semistandard tableaux —to Gelfand-Tsetlin pattern⟶ Gelfand-Tsetlin patterns
St000114: Gelfand-Tsetlin patterns ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 18%

Values

[1] => [[1]]
 => [[1]]
 => [[1]]
 => 1
[1,2] => [[1,0],[0,1]]
 => [[1,1],[2]]
 => [[2,1],[2]]
 => 5
[2,1] => [[0,1],[1,0]]
 => [[1,2],[2]]
 => [[2,1],[1]]
 => 4
[1,2,3] => [[1,0,0],[0,1,0],[0,0,1]]
 => [[1,1,1],[2,2],[3]]
 => [[3,2,1],[3,2],[3]]
 => 14
[1,3,2] => [[1,0,0],[0,0,1],[0,1,0]]
 => [[1,1,1],[2,3],[3]]
 => [[3,2,1],[3,1],[3]]
 => 13
[2,1,3] => [[0,1,0],[1,0,0],[0,0,1]]
 => [[1,1,2],[2,2],[3]]
 => [[3,2,1],[3,2],[2]]
 => 13
[2,3,1] => [[0,0,1],[1,0,0],[0,1,0]]
 => [[1,1,3],[2,3],[3]]
 => [[3,2,1],[2,1],[2]]
 => 11
[3,1,2] => [[0,1,0],[0,0,1],[1,0,0]]
 => [[1,2,2],[2,3],[3]]
 => [[3,2,1],[3,1],[1]]
 => 11
[3,2,1] => [[0,0,1],[0,1,0],[1,0,0]]
 => [[1,2,3],[2,3],[3]]
 => [[3,2,1],[2,1],[1]]
 => 10
[1,2,3,4] => [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,2],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,3],[4]]
 => 30
[1,2,4,3] => [[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,1],[2,2,2],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,3],[4]]
 => 29
[1,3,2,4] => [[1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,1],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,2],[4]]
 => 29
[1,3,4,2] => [[1,0,0,0],[0,0,0,1],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,1],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,2],[4]]
 => 27
[1,4,2,3] => [[1,0,0,0],[0,0,1,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,1],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,1],[4]]
 => 27
[1,4,3,2] => [[1,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,1],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,1],[4]]
 => 26
[2,1,3,4] => [[0,1,0,0],[1,0,0,0],[0,0,1,0],[0,0,0,1]]
 => [[1,1,1,2],[2,2,2],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,3],[3]]
 => 29
[2,1,4,3] => [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]
 => [[1,1,1,2],[2,2,2],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,3],[3]]
 => 28
[2,3,1,4] => [[0,0,1,0],[1,0,0,0],[0,1,0,0],[0,0,0,1]]
 => [[1,1,1,3],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[3,2],[3]]
 => 27
[2,3,4,1] => [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]]
 => [[1,1,1,4],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,2],[3]]
 => 24
[2,4,1,3] => [[0,0,1,0],[1,0,0,0],[0,0,0,1],[0,1,0,0]]
 => [[1,1,1,3],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[3,1],[3]]
 => 25
[2,4,3,1] => [[0,0,0,1],[1,0,0,0],[0,0,1,0],[0,1,0,0]]
 => [[1,1,1,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,1],[3]]
 => 23
[3,1,2,4] => [[0,1,0,0],[0,0,1,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,2],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[4,2],[2]]
 => 27
[3,1,4,2] => [[0,1,0,0],[0,0,0,1],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,2],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,2],[2]]
 => 25
[3,2,1,4] => [[0,0,1,0],[0,1,0,0],[1,0,0,0],[0,0,0,1]]
 => [[1,1,2,3],[2,2,3],[3,3],[4]]
 => [[4,3,2,1],[4,3,2],[3,2],[2]]
 => 26
[3,2,4,1] => [[0,0,0,1],[0,1,0,0],[1,0,0,0],[0,0,1,0]]
 => [[1,1,2,4],[2,2,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,2],[2]]
 => 23
[3,4,1,2] => [[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,3],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[2,1],[2]]
 => 22
[3,4,2,1] => [[0,0,0,1],[0,0,1,0],[1,0,0,0],[0,1,0,0]]
 => [[1,1,3,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[2,1],[2]]
 => 21
[4,1,2,3] => [[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,2],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[4,1],[1]]
 => 24
[4,1,3,2] => [[0,1,0,0],[0,0,0,1],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,2],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[4,1],[1]]
 => 23
[4,2,1,3] => [[0,0,1,0],[0,1,0,0],[0,0,0,1],[1,0,0,0]]
 => [[1,2,2,3],[2,3,3],[3,4],[4]]
 => [[4,3,2,1],[4,3,1],[3,1],[1]]
 => 23
[4,2,3,1] => [[0,0,0,1],[0,1,0,0],[0,0,1,0],[1,0,0,0]]
 => [[1,2,2,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[3,1],[1]]
 => 21
[4,3,1,2] => [[0,0,1,0],[0,0,0,1],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,3],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[4,2,1],[2,1],[1]]
 => 21
[4,3,2,1] => [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,0]]
 => [[1,2,3,4],[2,3,4],[3,4],[4]]
 => [[4,3,2,1],[3,2,1],[2,1],[1]]
 => 20
[1,2,3,4,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,4],[5]]
 => ? = 55
[1,2,3,5,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,4],[5]]
 => ? = 54
[1,2,4,3,5] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,4],[5]]
 => ? = 54
[1,2,4,5,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,2],[5,4],[5]]
 => ? = 52
[1,2,5,3,4] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,1],[5,4],[5]]
 => ? = 52
[1,2,5,4,3] => [[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,1],[5,4],[5]]
 => ? = 51
[1,3,2,4,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,3],[5]]
 => ? = 54
[1,3,2,5,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,3],[5]]
 => ? = 53
[1,3,4,2,5] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,3],[5]]
 => ? = 52
[1,3,4,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,3,2,1],[5,3,2],[5,3],[5]]
 => ? = 49
[1,3,5,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,3,1],[5,3],[5]]
 => ? = 50
[1,3,5,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,3,2,1],[5,3,1],[5,3],[5]]
 => ? = 48
[1,4,2,3,5] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,2],[5]]
 => ? = 52
[1,4,2,5,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,2],[5,2],[5]]
 => ? = 50
[1,4,3,2,5] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,3,2],[5,2],[5]]
 => ? = 51
[1,4,3,5,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,3,2,1],[5,3,2],[5,2],[5]]
 => ? = 48
[1,4,5,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,2,1],[5,2],[5]]
 => ? = 47
[1,4,5,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
 => [[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,3,2,1],[5,2,1],[5,2],[5]]
 => ? = 46
[1,5,2,3,4] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,3,3],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,1],[5,1],[5]]
 => ? = 49
[1,5,2,4,3] => [[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,3,3],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,1],[5,1],[5]]
 => ? = 48
[1,5,3,2,4] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,3,1],[5,1],[5]]
 => ? = 48
[1,5,3,4,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,3,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,3,2,1],[5,3,1],[5,1],[5]]
 => ? = 46
[1,5,4,2,3] => [[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,4,4],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,2,1],[5,1],[5]]
 => ? = 46
[1,5,4,3,2] => [[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
 => [[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,3,2,1],[5,2,1],[5,1],[5]]
 => ? = 45
[2,1,3,4,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,4],[4]]
 => ? = 54
[2,1,3,5,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,4],[4]]
 => ? = 53
[2,1,4,3,5] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[5,4],[4]]
 => ? = 53
[2,1,4,5,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,2],[5,4],[4]]
 => ? = 51
[2,1,5,3,4] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,0,1,0,0]]
 => [[1,1,1,1,2],[2,2,2,2],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,1],[5,4],[4]]
 => ? = 51
[2,1,5,4,3] => [[0,1,0,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0]]
 => [[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,1],[5,4],[4]]
 => ? = 50
[2,3,1,4,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[4,3],[4]]
 => ? = 52
[2,3,1,5,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[4,3],[4]]
 => ? = 51
[2,3,4,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[4,3],[4]]
 => ? = 49
[2,3,4,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[4,3,2,1],[4,3,2],[4,3],[4]]
 => ? = 45
[2,3,5,1,4] => [[0,0,0,1,0],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,0,1],[0,0,1,0,0]]
 => [[1,1,1,1,4],[2,2,2,4],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[4,3,1],[4,3],[4]]
 => ? = 47
[2,3,5,4,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,1,0,0,0],[0,0,0,1,0],[0,0,1,0,0]]
 => [[1,1,1,1,5],[2,2,2,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[4,3,2,1],[4,3,1],[4,3],[4]]
 => ? = 44
[2,4,1,3,5] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,2],[4,2],[4]]
 => ? = 50
[2,4,1,5,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,2],[4,2],[4]]
 => ? = 48
[2,4,3,1,5] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,0,1]]
 => [[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[4,3,2],[4,2],[4]]
 => ? = 48
[2,4,3,5,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,1,0,0,0],[0,0,0,1,0]]
 => [[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]]
 => [[5,4,3,2,1],[4,3,2,1],[4,3,2],[4,2],[4]]
 => ? = 44
[2,4,5,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,1,0,0,0],[0,0,1,0,0]]
 => [[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[4,2,1],[4,2],[4]]
 => ? = 44
[2,4,5,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,1,0,0,0],[0,0,1,0,0]]
 => [[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[4,3,2,1],[4,2,1],[4,2],[4]]
 => ? = 42
[2,5,1,3,4] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1],[0,1,0,0,0]]
 => [[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,1],[4,1],[4]]
 => ? = 47
[2,5,1,4,3] => [[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0],[0,1,0,0,0]]
 => [[1,1,1,1,3],[2,3,3,3],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[5,4,1],[4,1],[4]]
 => ? = 46
[2,5,3,1,4] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,0,1],[0,1,0,0,0]]
 => [[1,1,1,1,4],[2,3,3,4],[3,4,4],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[4,3,1],[4,1],[4]]
 => ? = 45
[2,5,3,4,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,1,0,0,0]]
 => [[1,1,1,1,5],[2,3,3,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[4,3,2,1],[4,3,1],[4,1],[4]]
 => ? = 42
[2,5,4,1,3] => [[0,0,0,1,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,1,0,0],[0,1,0,0,0]]
 => [[1,1,1,1,4],[2,3,4,4],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,2,1],[4,2,1],[4,1],[4]]
 => ? = 43
[2,5,4,3,1] => [[0,0,0,0,1],[1,0,0,0,0],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0]]
 => [[1,1,1,1,5],[2,3,4,5],[3,4,5],[4,5],[5]]
 => [[5,4,3,2,1],[4,3,2,1],[4,2,1],[4,1],[4]]
 => ? = 41
[3,1,2,4,5] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,1,0],[0,0,0,0,1]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]]
 => [[5,4,3,2,1],[5,4,3,2],[5,4,3],[5,3],[3]]
 => ? = 52
[3,1,2,5,4] => [[0,1,0,0,0],[0,0,1,0,0],[1,0,0,0,0],[0,0,0,0,1],[0,0,0,1,0]]
 => [[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]]
 => [[5,4,3,2,1],[5,4,3,1],[5,4,3],[5,3],[3]]
 => ? = 51

Description

The sum of the entries of the Gelfand-Tsetlin pattern.

Matching statistic: St001168
(load all 12 compositions to match this statistic)

Mapping

St001168: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 16%

Values

[1] => ? = 1
[1,2] => 5
[2,1] => 4
[1,2,3] => 14
[1,3,2] => 13
[2,1,3] => 13
[2,3,1] => 11
[3,1,2] => 11
[3,2,1] => 10
[1,2,3,4] => ? = 30
[1,2,4,3] => 29
[1,3,2,4] => 29
[1,3,4,2] => 27
[1,4,2,3] => 27
[1,4,3,2] => 26
[2,1,3,4] => 29
[2,1,4,3] => 28
[2,3,1,4] => 27
[2,3,4,1] => 24
[2,4,1,3] => 25
[2,4,3,1] => 23
[3,1,2,4] => 27
[3,1,4,2] => 25
[3,2,1,4] => 26
[3,2,4,1] => 23
[3,4,1,2] => 22
[3,4,2,1] => 21
[4,1,2,3] => 24
[4,1,3,2] => 23
[4,2,1,3] => 23
[4,2,3,1] => 21
[4,3,1,2] => 21
[4,3,2,1] => 20
[1,2,3,4,5] => ? = 55
[1,2,3,5,4] => ? = 54
[1,2,4,3,5] => ? = 54
[1,2,4,5,3] => ? = 52
[1,2,5,3,4] => ? = 52
[1,2,5,4,3] => ? = 51
[1,3,2,4,5] => ? = 54
[1,3,2,5,4] => ? = 53
[1,3,4,2,5] => ? = 52
[1,3,4,5,2] => ? = 49
[1,3,5,2,4] => ? = 50
[1,3,5,4,2] => ? = 48
[1,4,2,3,5] => ? = 52
[1,4,2,5,3] => ? = 50
[1,4,3,2,5] => ? = 51
[1,4,3,5,2] => ? = 48
[1,4,5,2,3] => ? = 47
[1,4,5,3,2] => ? = 46
[1,5,2,3,4] => ? = 49
[1,5,2,4,3] => ? = 48
[1,5,3,2,4] => ? = 48
[1,5,3,4,2] => ? = 46
[1,5,4,2,3] => ? = 46
[1,5,4,3,2] => ? = 45
[2,1,3,4,5] => ? = 54
[2,1,3,5,4] => ? = 53
[2,1,4,3,5] => ? = 53
[2,1,4,5,3] => ? = 51
[2,1,5,3,4] => ? = 51
[2,1,5,4,3] => ? = 50
[2,3,1,4,5] => ? = 52
[2,3,1,5,4] => ? = 51
[2,3,4,1,5] => ? = 49
[2,3,4,5,1] => ? = 45
[2,3,5,1,4] => ? = 47
[2,3,5,4,1] => ? = 44
[2,4,1,3,5] => ? = 50
[2,4,1,5,3] => ? = 48
[2,4,3,1,5] => ? = 48
[2,4,3,5,1] => ? = 44
[2,4,5,1,3] => ? = 44
[2,4,5,3,1] => ? = 42
[2,5,1,3,4] => ? = 47
[2,5,1,4,3] => ? = 46
[2,5,3,1,4] => ? = 45
[2,5,3,4,1] => ? = 42
[2,5,4,1,3] => ? = 43
[2,5,4,3,1] => ? = 41

Description

The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of

$K[x]/(x^n)$ .