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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2502.10727 |
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| _version_ | 1866929717360197632 |
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| author | Pan, Ran Remmel, Jeffrey |
| author_facet | Pan, Ran Remmel, Jeffrey |
| contents | In this paper, we use Hasse diagrams and generating functions to count alternating permutations with restricted prefix and suffix of lengths 3 and 4. In other words, for an alternating permutation $σ=σ_1σ_2σ_3\cdotsσ_{n}\in S_{n}$, we restrict length-3 prefixes $σ_1σ_2σ_3$ to follow certain patterns, such as $231$ and $132$, or follow certain restrictions such as $σ_2 \geq \max\{σ_1,σ_3\}+2$, similarly for prefixes of length 4. We also study the enumeration of alternating permutations with restrictions on both prefix and suffix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting alternating permutations with restricted prefix and suffix Pan, Ran Remmel, Jeffrey Combinatorics In this paper, we use Hasse diagrams and generating functions to count alternating permutations with restricted prefix and suffix of lengths 3 and 4. In other words, for an alternating permutation $σ=σ_1σ_2σ_3\cdotsσ_{n}\in S_{n}$, we restrict length-3 prefixes $σ_1σ_2σ_3$ to follow certain patterns, such as $231$ and $132$, or follow certain restrictions such as $σ_2 \geq \max\{σ_1,σ_3\}+2$, similarly for prefixes of length 4. We also study the enumeration of alternating permutations with restrictions on both prefix and suffix. |
| title | Counting alternating permutations with restricted prefix and suffix |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2502.10727 |