SmallerChildPathLeafLabel on Permutation
The label of the leaf reached from the root of the increasing binary tree of p by always following the child with the smaller label.
The root of a window is its minimum, and the smaller child is the root of the side holding the second smallest entry (St000724).
Called as CombinatorialStat(x, "SmallerChildPathLeafLabel"). The head's page has its examples.
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FindStat St000724
The label of the leaf of the path following the smaller label in the increasing binary tree associated to a permutation.
| Object | Value |
|---|---|
[1,2] | 2 |
[2,1] | 2 |
[1,2,3] | 3 |
[1,3,2] | 3 |
[2,1,3] | 2 |
[2,3,1] | 3 |
[3,1,2] | 2 |
[3,2,1] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000724 has the rest.