Characterizing avoidance in cycles via vincular patterns
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918014450925568 |
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| author | Laudone, Robert P. |
| author_facet | Laudone, Robert P. |
| contents | We show that cyclic permutations avoiding $321$ are precisely those permutations whose image under the fundamental bijection avoid a set of vincular patterns. We do this by using pattern functions and arrow patterns, in combination with the characterization of $321$ avoidance in terms of equality of the upper bound of the Daiconis-Graham inequalities. We then explore some consequences of this result, including upper and lower bound results on the growth rate of $321$ avoiding cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing avoidance in cycles via vincular patterns Laudone, Robert P. Combinatorics 05A05, 05A15 We show that cyclic permutations avoiding $321$ are precisely those permutations whose image under the fundamental bijection avoid a set of vincular patterns. We do this by using pattern functions and arrow patterns, in combination with the characterization of $321$ avoidance in terms of equality of the upper bound of the Daiconis-Graham inequalities. We then explore some consequences of this result, including upper and lower bound results on the growth rate of $321$ avoiding cycles. |
| title | Characterizing avoidance in cycles via vincular patterns |
| topic | Combinatorics 05A05, 05A15 |
| url | https://arxiv.org/abs/2505.05651 |