The rix statistic of a permutation.
This statistic is defined recursively as follows: $rix([]) = 0$, and if $w_i = \max\{w_1, w_2,\dots, w_k\}$, then
$rix(w) := 0$ if $i = 1 < k$,
$rix(w) := 1 + rix(w_1,w_2,\dots,w_{k−1})$ if $i = k$ and
$rix(w) := rix(w_{i+1},w_{i+2},\dots,w_k)$ if $1 < i < k$.

Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.

This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.

Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.