BoundaryNodes on BinaryTree
The number of nodes on the left spine or the right spine, the root counted once.
FindStat calls these the external nodes; the name stays off the empty subtrees, which are Knuth's.
Called as CombinatorialStat(x, "BoundaryNodes"). 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 St000203
The number of external nodes of a binary tree.
| Object | Value |
|---|---|
[.,.] | 1 |
[.,[.,.]] | 2 |
[[.,.],.] | 2 |
[.,[.,[.,.]]] | 3 |
[.,[[.,.],.]] | 2 |
[[.,.],[.,.]] | 3 |
[[.,[.,.]],.] | 2 |
[[[.,.],.],.] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000203 has the rest.