Permutations with a fixed number of occurrences of a monotone pattern
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917046897344512 |
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| author | Waite, Michael |
| author_facet | Waite, Michael |
| contents | We bound the number of permutations with a fixed number $r$ of $321 \ominus p_0$ patterns by a constant times the number of permutations which avoid $321 \ominus p_0$. We use this new upper bound to show that the ordinary generating function for permutations with $r$ copies of $k(k-1)...1$ is not rational for odd $k \geq 3$ and not algebraic for even $k \geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permutations with a fixed number of occurrences of a monotone pattern Waite, Michael Combinatorics 05A05, 05A15, 05A20 We bound the number of permutations with a fixed number $r$ of $321 \ominus p_0$ patterns by a constant times the number of permutations which avoid $321 \ominus p_0$. We use this new upper bound to show that the ordinary generating function for permutations with $r$ copies of $k(k-1)...1$ is not rational for odd $k \geq 3$ and not algebraic for even $k \geq 3$. |
| title | Permutations with a fixed number of occurrences of a monotone pattern |
| topic | Combinatorics 05A05, 05A15, 05A20 |
| url | https://arxiv.org/abs/2506.05712 |