Snake Graphs from Triangulated Orbifolds
We give an explicit combinatorial formula for the Laurent expansion of any arc or closed curve on an unpunctured triangulated orbifold. We do this by extending the snake graph construction of Musiker, Schiffler, and Williams to unpunctured orbifolds. In the case of an ordinary arc, this gives a comb...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211081 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Snake Graphs from Triangulated Orbifolds. Esther Banaian and Elizabeth Kelley. SIGMA 16 (2020), 138, 50 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732579136864256 |
|---|---|
| author | Banaian, Esther Kelley, Elizabeth |
| author_facet | Banaian, Esther Kelley, Elizabeth |
| citation_txt | Snake Graphs from Triangulated Orbifolds. Esther Banaian and Elizabeth Kelley. SIGMA 16 (2020), 138, 50 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give an explicit combinatorial formula for the Laurent expansion of any arc or closed curve on an unpunctured triangulated orbifold. We do this by extending the snake graph construction of Musiker, Schiffler, and Williams to unpunctured orbifolds. In the case of an ordinary arc, this gives a combinatorial proof of positivity to the generalized cluster algebra from this orbifold.
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| first_indexed | 2026-04-17T15:36:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211081 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:36:59Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Banaian, Esther Kelley, Elizabeth 2025-12-23T13:11:38Z 2020 Snake Graphs from Triangulated Orbifolds. Esther Banaian and Elizabeth Kelley. SIGMA 16 (2020), 138, 50 pages 1815-0659 2020 Mathematics Subject Classification: 05E15; 05C70; 16S99 arXiv:2003.13872 https://nasplib.isofts.kiev.ua/handle/123456789/211081 https://doi.org/10.3842/SIGMA.2020.138 We give an explicit combinatorial formula for the Laurent expansion of any arc or closed curve on an unpunctured triangulated orbifold. We do this by extending the snake graph construction of Musiker, Schiffler, and Williams to unpunctured orbifolds. In the case of an ordinary arc, this gives a combinatorial proof of positivity to the generalized cluster algebra from this orbifold. We would like to thank Gregg Musiker for many helpful discussions and his patient generosity in reading and providing feedback on many iterations of this paper. We would also like to thank the anonymous referees for their helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Snake Graphs from Triangulated Orbifolds Article published earlier |
| spellingShingle | Snake Graphs from Triangulated Orbifolds Banaian, Esther Kelley, Elizabeth |
| title | Snake Graphs from Triangulated Orbifolds |
| title_full | Snake Graphs from Triangulated Orbifolds |
| title_fullStr | Snake Graphs from Triangulated Orbifolds |
| title_full_unstemmed | Snake Graphs from Triangulated Orbifolds |
| title_short | Snake Graphs from Triangulated Orbifolds |
| title_sort | snake graphs from triangulated orbifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211081 |
| work_keys_str_mv | AT banaianesther snakegraphsfromtriangulatedorbifolds AT kelleyelizabeth snakegraphsfromtriangulatedorbifolds |