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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2505.05218 |
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| _version_ | 1866918524233973760 |
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| author | Archer, Kassie Bourne, Noel |
| author_facet | Archer, Kassie Bourne, Noel |
| contents | A permutation $π$ is said to avoid a chain $(σ:τ)$ of patterns if $π$ avoids $σ$ and $π^2$ avoids $τ.$ In this paper, we define a notion of pattern avoidance for compositions of positive integers and use that idea to enumerate permutations of length $n$ that avoid the chain $(312,321:σ)$ for any pattern $σ\in \bigcup_{m\geq 1} S_m$. We also enumerate those permutations that avoid the chain $(312,4321:σ)$ for any $σ\in S_3.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pattern avoidance in compositions and powers of permutations Archer, Kassie Bourne, Noel Combinatorics A permutation $π$ is said to avoid a chain $(σ:τ)$ of patterns if $π$ avoids $σ$ and $π^2$ avoids $τ.$ In this paper, we define a notion of pattern avoidance for compositions of positive integers and use that idea to enumerate permutations of length $n$ that avoid the chain $(312,321:σ)$ for any pattern $σ\in \bigcup_{m\geq 1} S_m$. We also enumerate those permutations that avoid the chain $(312,4321:σ)$ for any $σ\in S_3.$ |
| title | Pattern avoidance in compositions and powers of permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.05218 |