TreeFactorial on OrderedTree
The product, over the vertices, of the number of vertices at or below each.
Called as CombinatorialStat(x, "TreeFactorial"). The head's page has its examples.
Live
Distribution
Over OrderedTrees at each size, tallied here in your browser; sizes past 6 are not offered.
Also on
The same name on other carriers, each its own implementation: BinaryTree.
FindStat St000410
The tree factorial of an ordered tree.
| Object | Value |
|---|---|
[[]] | 2 |
[[[]]] | 6 |
[[],[]] | 3 |
[[[[]]]] | 24 |
[[[],[]]] | 12 |
[[[]],[]] | 8 |
[[],[[]]] | 8 |
[[[[[]]]]] | 120 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000410 has the rest.