On the permutations that strongly avoid the pattern 312 or 231

2024/04/02 by Junyao Pan, Pengfei Guo, Pan, Junyao +1 · 2 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2404.01597

openalex publication_date 2024/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 2019, Bóna and Smith introduced the notion of strong pattern avoidance, that is, a permutation and its square both avoid a given pattern. In this paper, we enumerate the set of permutations π which not only strongly avoid the pattern 312 or 231 but also avoid the pattern τ, for τ∈ S₃ and some τ∈ S₄. One of them is to give a positive answer to a conjecture of Archer and Geary.

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• Pattern avoidance in compositions and powers of permutations
• On two conjectures about pattern avoidance of cyclic permutations

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