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RootDegree on OrderedTree ​

The number of children of the root.

On OrderedTree

Called as CombinatorialStat(x, "RootDegree"). 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 St000084

The number of subtrees.

ObjectValue
[[]]1
[[[]]]1
[[],[]]2
[[[[]]]]1
[[[],[]]]1
[[[]],[]]2
[[],[[]]]2
[[[[[]]]]]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000084 has the rest.