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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2509.17258 |
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| _version_ | 1866914169117212672 |
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| author | Adams, Ashleigh Banaian, Esther |
| author_facet | Adams, Ashleigh Banaian, Esther |
| contents | We exhibit two instances of the cyclic sieving phenomenon - one on dissections of a polygon of a fixed type and one on triangulations of a once-punctured polygon. We use these results to give refined enumerations of certain families of frieze patterns. We also give an interpretation of finite, positive integral frieze patterns fixed under nontrivial rotations as frieze patterns from a family of orbifolds and show that these are always unitary. Finally, we give a bijection between Holm-Jorgensen frieze patterns and p-Dyck paths, extending a recent construction of Canadas, Espinosa, Gaviria, and Rios, and discuss an induced rotation map on Dyck paths. Several conjectures and questions for future study are highlighted throughout the article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Cyclic Sieving Phenomenon and frieze patterns Adams, Ashleigh Banaian, Esther Combinatorics 05A30, 05A05, 13F60, 16G60 We exhibit two instances of the cyclic sieving phenomenon - one on dissections of a polygon of a fixed type and one on triangulations of a once-punctured polygon. We use these results to give refined enumerations of certain families of frieze patterns. We also give an interpretation of finite, positive integral frieze patterns fixed under nontrivial rotations as frieze patterns from a family of orbifolds and show that these are always unitary. Finally, we give a bijection between Holm-Jorgensen frieze patterns and p-Dyck paths, extending a recent construction of Canadas, Espinosa, Gaviria, and Rios, and discuss an induced rotation map on Dyck paths. Several conjectures and questions for future study are highlighted throughout the article. |
| title | The Cyclic Sieving Phenomenon and frieze patterns |
| topic | Combinatorics 05A30, 05A05, 13F60, 16G60 |
| url | https://arxiv.org/abs/2509.17258 |