Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000324
(load all 3 compositions to match this statistic)
Mapping
St000324: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 6
[1,2] => 18
[2,1] => 12
[1,2,3] => 54
[1,3,2] => 36
[2,1,3] => 36
[2,3,1] => 36
[3,1,2] => 36
[3,2,1] => 24
[1,2,3,4] => 162
[1,2,4,3] => 108
[1,3,2,4] => 108
[1,3,4,2] => 108
[1,4,2,3] => 108
[1,4,3,2] => 72
[2,1,3,4] => 108
[2,1,4,3] => 72
[2,3,1,4] => 36
[2,3,4,1] => 108
[2,4,1,3] => 36
[2,4,3,1] => 72
[3,1,2,4] => 108
[3,1,4,2] => 72
[3,2,1,4] => 72
[3,2,4,1] => 72
[3,4,1,2] => 36
[3,4,2,1] => 72
[4,1,2,3] => 108
[4,1,3,2] => 72
[4,2,1,3] => 72
[4,2,3,1] => 72
[4,3,1,2] => 72
[4,3,2,1] => 48
[1,2,3,4,5] => 486
[1,2,3,5,4] => 324
[1,2,4,3,5] => 324
[1,2,4,5,3] => 324
[1,2,5,3,4] => 324
[1,2,5,4,3] => 216
[1,3,2,4,5] => 324
[1,3,2,5,4] => 216
[1,3,4,2,5] => 108
[1,3,4,5,2] => 324
[1,3,5,2,4] => 108
[1,3,5,4,2] => 216
[1,4,2,3,5] => 324
[1,4,2,5,3] => 216
[1,4,3,2,5] => 216
[1,4,3,5,2] => 216
[1,4,5,2,3] => 108
Description
The shape of the tree associated to a permutation. A permutation can be mapped to a rooted tree with vertices {0,1,2,…,n} and root 0 in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1]. The statistic is given by $2^w 3^h$, where $w$ is the width [[St000325]] and $h$ is the height [[St000308]] of this tree.