SwapEquivalentTreeCount on BinaryTree
The number of binary trees that become this one when the children at any nodes are swapped: each node with different subtrees (an only child counts as different from the empty one) doubles the count.
FindStat's St000412: the binary trees with the same underlying unordered (rooted) tree.
Called as CombinatorialStat(x, "SwapEquivalentTreeCount"). 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 St000412
The number of binary trees with the same underlying unordered tree.
| Object | Value |
|---|---|
[.,[.,.]] | 2 |
[[.,.],.] | 2 |
[.,[.,[.,.]]] | 4 |
[.,[[.,.],.]] | 4 |
[[.,.],[.,.]] | 1 |
[[.,[.,.]],.] | 4 |
[[[.,.],.],.] | 4 |
[.,[.,[.,[.,.]]]] | 8 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000412 has the rest.