1
vote
1answer
146 views

Statistics on Lehmer codes

I am looking at words $\alpha_1 \ldots \alpha_n$, where $\alpha_j \in \{ 1, \ldots, j \}$. Thinking of $\alpha_j$ as a height, these words can be interpreted as left-to-right paths on the positive ...
17
votes
1answer
420 views

Salié permutations and fair permutations

In October 2010, I published a Monthly problem that introduced the concept of a fair permutation, which is a permutation $\pi$ such that for every $i$, either $\pi(i) > i$ and $\pi^{-1}(i) > i$, ...