6 problems

Gessel–Zhuang's conjecture. Every shuffle-compatible statistic is a descent statistic.

For a permutation $\tau$, let $\rm udr$, $\rm pk$, and $\rm des$ denote the permutation statistics of the length of the longest up-down run, the number of peaks, and the number of…

Grinberg's conjecture. The statistics $\operatorname{Lpk}$, $\operatorname{lpk}$, $\operatorname{Rpk}$, $\operatorname{rpk}$, $\operatorname{Val}$, and $\operatorname{val}$ are $M$…

Shuffle-compatibility conjecture. The pair

Let a permutation statistic be a statistic on permutations, and call it shuffle-compatible if the multiset of its values on shuffles of two permutations depends only on the two inp…

Let a permutation statistic assign an invariant to each permutation, and call it shuffle-compatible if, for any two disjoint permutations, the multiset of its values on their shuff…