HookNumber on BinaryTree
The number of hooks in the decomposition of the tree into hooks: a node with the chains of left children and of right children below it, the subtrees hanging off those chains decomposed in turn.
Called as CombinatorialStat(x, "HookNumber"). The head's page has its examples.
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Distribution
Over BinaryTrees at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000568
The hook number of a binary tree.
| Object | Value |
|---|---|
[.,[.,.]] | 1 |
[[.,.],.] | 1 |
[.,[.,[.,.]]] | 1 |
[.,[[.,.],.]] | 2 |
[[.,.],[.,.]] | 1 |
[[.,[.,.]],.] | 2 |
[[[.,.],.],.] | 1 |
[.,[.,[.,[.,.]]]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000568 has the rest.