Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001439
(load all 3 compositions to match this statistic)
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St001439: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1] => 1
[[1,2]]
 => [1,2] => 2
[[1],[2]]
 => [2,1] => 2
[[1,2,3]]
 => [1,2,3] => 3
[[1,3],[2]]
 => [2,1,3] => 3
[[1,2],[3]]
 => [3,1,2] => 2
[[1],[2],[3]]
 => [3,2,1] => 2
[[1,2,3,4]]
 => [1,2,3,4] => 4
[[1,3,4],[2]]
 => [2,1,3,4] => 4
[[1,2,4],[3]]
 => [3,1,2,4] => 3
[[1,2,3],[4]]
 => [4,1,2,3] => 3
[[1,3],[2,4]]
 => [2,4,1,3] => 2
[[1,2],[3,4]]
 => [3,4,1,2] => 2
[[1,4],[2],[3]]
 => [3,2,1,4] => 3
[[1,3],[2],[4]]
 => [4,2,1,3] => 3
[[1,2],[3],[4]]
 => [4,3,1,2] => 2
[[1],[2],[3],[4]]
 => [4,3,2,1] => 2
[[1,2,3,4,5]]
 => [1,2,3,4,5] => 5
[[1,3,4,5],[2]]
 => [2,1,3,4,5] => 5
[[1,2,4,5],[3]]
 => [3,1,2,4,5] => 4
[[1,2,3,5],[4]]
 => [4,1,2,3,5] => 4
[[1,2,3,4],[5]]
 => [5,1,2,3,4] => 3
[[1,3,5],[2,4]]
 => [2,4,1,3,5] => 3
[[1,2,5],[3,4]]
 => [3,4,1,2,5] => 3
[[1,3,4],[2,5]]
 => [2,5,1,3,4] => 2
[[1,2,4],[3,5]]
 => [3,5,1,2,4] => 2
[[1,2,3],[4,5]]
 => [4,5,1,2,3] => 2
[[1,4,5],[2],[3]]
 => [3,2,1,4,5] => 4
[[1,3,5],[2],[4]]
 => [4,2,1,3,5] => 4
[[1,2,5],[3],[4]]
 => [4,3,1,2,5] => 3
[[1,3,4],[2],[5]]
 => [5,2,1,3,4] => 3
[[1,2,4],[3],[5]]
 => [5,3,1,2,4] => 2
[[1,2,3],[4],[5]]
 => [5,4,1,2,3] => 2
[[1,4],[2,5],[3]]
 => [3,2,5,1,4] => 4
[[1,3],[2,5],[4]]
 => [4,2,5,1,3] => 4
[[1,2],[3,5],[4]]
 => [4,3,5,1,2] => 3
[[1,3],[2,4],[5]]
 => [5,2,4,1,3] => 4
[[1,2],[3,4],[5]]
 => [5,3,4,1,2] => 3
[[1,5],[2],[3],[4]]
 => [4,3,2,1,5] => 3
[[1,4],[2],[3],[5]]
 => [5,3,2,1,4] => 2
[[1,3],[2],[4],[5]]
 => [5,4,2,1,3] => 2
[[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => 3
[[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => 3
[[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => 6
[[1,3,4,5,6],[2]]
 => [2,1,3,4,5,6] => 6
[[1,2,4,5,6],[3]]
 => [3,1,2,4,5,6] => 5
[[1,2,3,5,6],[4]]
 => [4,1,2,3,5,6] => 5
[[1,2,3,4,6],[5]]
 => [5,1,2,3,4,6] => 4
[[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => 4
[[1,3,5,6],[2,4]]
 => [2,4,1,3,5,6] => 4
Description
The number of even weak deficiencies and of odd weak exceedences. For a permutation $\sigma$, this is the number of indices $i$ such that $\sigma(i) \leq i$ if $i$ is even and $\sigma(i) \geq i$ if $i$ is odd. According to [1], $\sigma$ is a '''D-permutation''' if all indices have this property and the coefficients of the characteristic polynomial of the homogenized linial arrangement are given by the number of D-permutations with a given number of cycles.