Schur-Concavity for Avoidance of Increasing Subsequences in Block-Ascending Permutations

Abstract

For integers $a_1,\dots ,a_n\ge 0$ and $k\ge 1$, let ${\mathcal{L}}_{k+2}(a_1,\dots ,a_n)$ denote the set of permutations of $\{1,\dots ,a_1+\cdots +a_n\}$ whose descent set is contained in $\{a_1,a_1+a_2,\dots ,a_1+\cdots +a_{n-1}\}$, and which avoids the pattern $12\dots (k+2)$. We exhibit some bijections between such sets, most notably showing that $\#{\mathcal{L}}_{k+2}(a_1,\dots ,a_n)$ is symmetric in the $a_i$ and is in fact Schur-concave. This generalizes a set of equivalences observed by Mei and Wang.

arXiv comment11 pages, incorporated suggestions and corrections from anonymous referee

Cited by in corpus (1)

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