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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.01597 |
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| _version_ | 1866910395624587264 |
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| author | Pan, Junyao Guo, Pengfei |
| author_facet | Pan, Junyao Guo, Pengfei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01597 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the permutations that strongly avoid the pattern 312 or 231 Pan, Junyao Guo, Pengfei Combinatorics 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. |
| title | On the permutations that strongly avoid the pattern 312 or 231 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.01597 |