$k$-pop stack sortable permutations and $2$-avoidance

Abstract

We consider permutations sortable by k passes through a deterministic pop stack. We show that for any k ∈ N the set is characterised by finitely many patterns, answering a question of Claesson and Guðmundsson.Our characterisation demands a more precise definition than in previous literature of what it means for a permutation to avoid a set of barred and unbarred patterns. We propose a new notion called 2-avoidance.