Highly sorted permutations with respect to a 312-avoiding stack

Let s 312 be the generalized stack-sorting map, where instead of being required to increase, the stack avoids the pattern 312.In this note, we give a simple characterization of the set s n-2 312 (S n ) for all n, the consequence of which is that |s n-2 312 (S n )| = 2 n-1 + 1.As a corollary, we settle a conjecture by Defant and Zheng.

Abstract licence: CC BY-ND

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