LongestPathVertexCount on OrderedTree
The most vertices on a path from the root: the height plus one.
FindStat calls this the depth of an ordered tree.
Called as CombinatorialStat(x, "LongestPathVertexCount"). 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.
FindStat St000094
The depth of an ordered tree.
| Object | Value |
|---|---|
[[]] | 2 |
[[[]]] | 3 |
[[],[]] | 2 |
[[[[]]]] | 4 |
[[[],[]]] | 3 |
[[[]],[]] | 3 |
[[],[[]]] | 3 |
[[[[[]]]]] | 5 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000094 has the rest.