3 problems

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…

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…