T-Path Formula and Atomic Bases for Cluster Algebras of Type D
We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D.
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147131 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | T-Path Formula and Atomic Bases for Cluster Algebras of Type D / E. Gunawan, G. Musiker // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862548173157826560 |
|---|---|
| author | Gunawan, E. Musiker, G. |
| author_facet | Gunawan, E. Musiker, G. |
| citation_txt | T-Path Formula and Atomic Bases for Cluster Algebras of Type D / E. Gunawan, G. Musiker // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D.
|
| first_indexed | 2025-11-25T18:52:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147131 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T18:52:24Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gunawan, E. Musiker, G. 2019-02-13T17:16:42Z 2019-02-13T17:16:42Z 2015 T-Path Formula and Atomic Bases for Cluster Algebras of Type D / E. Gunawan, G. Musiker // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 23 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 13F60; 05E15; 16S99 DOI:10.3842/SIGMA.2015.060 https://nasplib.isofts.kiev.ua/handle/123456789/147131 We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type D. This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
 available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
 The authors would like to thank Pasha Pylyavskyy, Vic Reiner, and Peter Webb for looking over
 an early version of this paper, Hugh Thomas for helpful discussions, and the referees for many
 useful comments. The authors were supported by NSF Grants DMS-1067183 and DMS-1148634. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications T-Path Formula and Atomic Bases for Cluster Algebras of Type D Article published earlier |
| spellingShingle | T-Path Formula and Atomic Bases for Cluster Algebras of Type D Gunawan, E. Musiker, G. |
| title | T-Path Formula and Atomic Bases for Cluster Algebras of Type D |
| title_full | T-Path Formula and Atomic Bases for Cluster Algebras of Type D |
| title_fullStr | T-Path Formula and Atomic Bases for Cluster Algebras of Type D |
| title_full_unstemmed | T-Path Formula and Atomic Bases for Cluster Algebras of Type D |
| title_short | T-Path Formula and Atomic Bases for Cluster Algebras of Type D |
| title_sort | t-path formula and atomic bases for cluster algebras of type d |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147131 |
| work_keys_str_mv | AT gunawane tpathformulaandatomicbasesforclusteralgebrasoftyped AT musikerg tpathformulaandatomicbasesforclusteralgebrasoftyped |