Permutations with a fixed number of occurrences of a pattern: A case generalizing 231
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908906733699072 |
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| author | Waite, Michael |
| author_facet | Waite, Michael |
| contents | We determine a set of permutation patterns $q$ so that the number of permutations with $r$ occurrences of $q$ is asymptotically $n^r$ times the number of permutations avoiding $q$, partially settling a conjecture of Conway and Guttman. We also use these asymptotics to prove nonrationality and nonalgebraicity for certain ordinary generating functions for permutations with $r$ copies of a pattern. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21625 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Permutations with a fixed number of occurrences of a pattern: A case generalizing 231 Waite, Michael Combinatorics 05A05, 05A15, 05A20 We determine a set of permutation patterns $q$ so that the number of permutations with $r$ occurrences of $q$ is asymptotically $n^r$ times the number of permutations avoiding $q$, partially settling a conjecture of Conway and Guttman. We also use these asymptotics to prove nonrationality and nonalgebraicity for certain ordinary generating functions for permutations with $r$ copies of a pattern. |
| title | Permutations with a fixed number of occurrences of a pattern: A case generalizing 231 |
| topic | Combinatorics 05A05, 05A15, 05A20 |
| url | https://arxiv.org/abs/2603.21625 |