9 problems

Conjectures. For $E=E[\overline{123}]$ and for $E=E[\overline{213}]$, respectively,

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 $n\geq0$,

Wilf-equivalence conjecture. The following Wilf-equivalences hold:

A permutation statistic is Mahonian if, on permutations in $\mathfrak{S}_n$, it has the same distribution as the major index. The vincular-pattern statistic … was conjectured to be…

A permutation statistic is Mahonian if, on permutations in $\mathfrak{S}_n$, it has the same distribution as the major index. The vincular-pattern statistic … was conjectured to be…

A permutation statistic is Mahonian if, on permutations in $\mathfrak{S}_n$, it has the same distribution as the major index. The vincular-pattern statistic … was conjectured to be…

For consecutive permutation patterns, write $sigma\stackrel{fs}{\sim}\tau$ when $sigma$ and $tau$ are filling-shape-Wilf-equivalent, meaning that they are avoided by fillings of ev…

A vincular pattern is a permutation pattern in which selected adjacent entries are required to occur consecutively; write $sigma\sim\tau$ when two patterns are Wilf-equivalent, mea…