5 problems

Enumeration conjecture.

For each $n\geq0$, let $a_{n,k}$ and $b_{n,k}$ be the distributions defined by counting occurrences of $2\text{-}31$ on $\mathfrak{D}^1_{2n}(2143)$ and occurrences of $13\text{-}2$…

Burstein–Jones's dominance conjecture. For all $n\geq0$,

Let $\mathfrak{D}^1_{2n}$ denote the set of Dumont-1 permutations of length $2n$, and let $\mathfrak{D}^1_{2n}(\tau)$ denote those avoiding the pattern $\tau$. Burstein–Jones's Wil…

A permutation has a descent from an even value to an even value when two consecutive entries form a descent and both values are even. The authors consider the sets of permutations…