2 problems

Let $B_n$ denote the set of binary trees with $n$ leaves. For a binary tree $T$, let $l(T)$ be its number of leaves and $k(T)$ its number of symmetries, meaning vertices with ident…

A cherry is a pair of leaves joined to a common parent in a binary tree. Let a tanglegram of size $n$ be chosen uniformly at random, and consider its left binary tree. Cherry-count…