AutomorphismGroupSize on OrderedTree
The number of ways to permute identical children, at every vertex at once: the product, over the vertices, of the factorials of how many times each child tree occurs.
Called as CombinatorialStat(x, "AutomorphismGroupSize"). 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 St000417
The size of the automorphism group of the ordered tree.
| Object | Value |
|---|---|
[[]] | 1 |
[[[]]] | 1 |
[[],[]] | 2 |
[[[[]]]] | 1 |
[[[],[]]] | 2 |
[[[]],[]] | 1 |
[[],[[]]] | 1 |
[[[[[]]]]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000417 has the rest.