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

For integers a1, . . . , an > 0 and k > 1, let Lk+2(a1, . . . , an) denote the set of permutations of {1, . . . , a1 + · · · + an} whose descent set is contained in {a1, a1 + a2, . . . , a1+ · · ·+an−1}, and which avoids the pattern 12 . . . (k+2). We exhibit some bijections between such sets, most notably showing that #Lk+2(a1, . . . , an) is symmetric in the ai and is in fact Schur-concave. This generalizes a set of equivalences observed by Mei and Wang.