Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000726
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Mapping
St000726: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 2
[2,3,1] => 0
[3,1,2] => 2
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 3
[1,3,4,2] => 0
[1,4,2,3] => 3
[1,4,3,2] => 0
[2,1,3,4] => 2
[2,1,4,3] => 2
[2,3,1,4] => 3
[2,3,4,1] => 0
[2,4,1,3] => 3
[2,4,3,1] => 0
[3,1,2,4] => 3
[3,1,4,2] => 3
[3,2,1,4] => 3
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 0
[4,1,2,3] => 3
[4,1,3,2] => 3
[4,2,1,3] => 3
[4,2,3,1] => 3
[4,3,1,2] => 2
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 4
[1,2,4,5,3] => 0
[1,2,5,3,4] => 4
[1,2,5,4,3] => 0
[1,3,2,4,5] => 3
[1,3,2,5,4] => 3
[1,3,4,2,5] => 4
[1,3,4,5,2] => 0
[1,3,5,2,4] => 4
[1,3,5,4,2] => 0
[1,4,2,3,5] => 4
[1,4,2,5,3] => 4
[1,4,3,2,5] => 4
[1,4,3,5,2] => 4
[1,4,5,2,3] => 3
[1,4,5,3,2] => 0
Description
The normalized sum of the leaf labels of the increasing binary tree associated to a permutation. The sum of the leaf labels is at least the size of the permutation, equality is attained for the binary trees that have only one leaf. This statistic is the sum of the leaf labels minus the size of the permutation.