On a question about pattern avoidance of cyclic permutations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912948291633152 |
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| author | Zhang, Zuo-Ru Zhao, Hongkuan |
| author_facet | Zhang, Zuo-Ru Zhao, Hongkuan |
| contents | Recently, Archer et al.\ studied cyclic permutations that avoid the decreasing pattern $δ_k=k(k-1)\cdots21$ in one-line notation and avoid another pattern $τ$ of length $4$ in all their cycle forms. There are three cases in total to consider, namely, $τ=1324, 1342$ and $1432$. They determined two of them, leaving the case $τ=1432$ as an open question. In this paper, we resolve this case by deriving explicit formulas based on an analysis of the structure of cycle forms and an application of Dilworth's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06269 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a question about pattern avoidance of cyclic permutations Zhang, Zuo-Ru Zhao, Hongkuan Combinatorics 05A05, 05A15 Recently, Archer et al.\ studied cyclic permutations that avoid the decreasing pattern $δ_k=k(k-1)\cdots21$ in one-line notation and avoid another pattern $τ$ of length $4$ in all their cycle forms. There are three cases in total to consider, namely, $τ=1324, 1342$ and $1432$. They determined two of them, leaving the case $τ=1432$ as an open question. In this paper, we resolve this case by deriving explicit formulas based on an analysis of the structure of cycle forms and an application of Dilworth's theorem. |
| title | On a question about pattern avoidance of cyclic permutations |
| topic | Combinatorics 05A05, 05A15 |
| url | https://arxiv.org/abs/2603.06269 |