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arXiv · 2404.01597

On the permutations that strongly avoid the pattern 312 or 231

Junyao Pan·Pengfei Guo
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Abstract

In 2019, Bóna and Smith introduced the notion of \emph{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 $τ\in S_3$ and some $τ\in S_4$. One of them is to give a positive answer to a conjecture of Archer and Geary.

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Junyao Pan, Pengfei Guo. 2024-04-02. On the permutations that strongly avoid the pattern 312 or 231. https://arxiv.org/abs/2404.01597

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