ProtectionNumber on BinaryTree

The edges from the root to the nearest leaf, a binary tree's empty subtree counting as a leaf.

On BinaryTree

Called as CombinatorialStat(x, "ProtectionNumber"). The head's page has its examples.

Live

Distribution

Over BinaryTrees at each size, tallied here in your browser; sizes past 6 are not offered.

Sizes 1 to

Also on

The same name on other carriers, each its own implementation: OrderedTree.

FindStat St000701

The protection number of a binary tree.

Object	Value
[.,.]	1
[.,[.,.]]	1
[[.,.],.]	1
[.,[.,[.,.]]]	1
[.,[[.,.],.]]	1
[[.,.],[.,.]]	2
[[.,[.,.]],.]	1
[[[.,.],.],.]	1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000701 has the rest.