Powers of permutations that avoid chains of patterns

2023/12/22 by Kassie Archer, Archer, Kassie, Aaron Geary +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2312.14351

openalex publication_date 2023/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a recent paper, Bona and Smith define the notion of strong avoidance, in which a permutation and its square both avoid a given pattern. In this paper, we generalize this idea to what we call chain avoidance. We say that a permutation avoids a chain of patterns (τ₁ : τ₂: ⋯ : τ_k) if the i-th power of the permutation avoids the pattern τ_i. We enumerate the set of permutations π which avoid the chain (213, 312 : τ), i.e.,~unimodal permutations whose square avoids τ, for τ∈ §₃ and use this to find a lower bound on the number of permutations that avoid the chain (312: τ) for τ∈ §₃. We finish the paper by discussing permutations that avoid longer chains.

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