Q-system Cluster Algebras, Paths and Total Positivity
In the first part of this paper, we provide a concise review of our method of solution of the Ar Q-systems in terms of the partition function of paths on a weighted graph. In the second part, we show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connecti...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2010 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146152 |
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| Цитувати: | Q-system Cluster Algebras, Paths and Total Positivity / P. di Francesco, R. Kedem // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146152 |
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dspace |
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irk-123456789-1461522019-02-08T01:23:23Z Q-system Cluster Algebras, Paths and Total Positivity di Francesko, P. Kedem, R. In the first part of this paper, we provide a concise review of our method of solution of the Ar Q-systems in terms of the partition function of paths on a weighted graph. In the second part, we show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connection to the theory of planar networks introduced in the context of totally positive matrices by Fomin and Zelevinsky. As an illustration of the further generality of our method, we apply it to give a simple solution for the rank 2 affine cluster algebras studied by Caldero and Zelevinsky. 2010 Article Q-system Cluster Algebras, Paths and Total Positivity / P. di Francesco, R. Kedem // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05E10; 13F16; 82B20 http://dspace.nbuv.gov.ua/handle/123456789/146152 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In the first part of this paper, we provide a concise review of our method of solution of the Ar Q-systems in terms of the partition function of paths on a weighted graph. In the second part, we show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connection to the theory of planar networks introduced in the context of totally positive matrices by Fomin and Zelevinsky. As an illustration of the further generality of our method, we apply it to give a simple solution for the rank 2 affine cluster algebras studied by Caldero and Zelevinsky. |
| format |
Article |
| author |
di Francesko, P. Kedem, R. |
| spellingShingle |
di Francesko, P. Kedem, R. Q-system Cluster Algebras, Paths and Total Positivity Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
di Francesko, P. Kedem, R. |
| author_sort |
di Francesko, P. |
| title |
Q-system Cluster Algebras, Paths and Total Positivity |
| title_short |
Q-system Cluster Algebras, Paths and Total Positivity |
| title_full |
Q-system Cluster Algebras, Paths and Total Positivity |
| title_fullStr |
Q-system Cluster Algebras, Paths and Total Positivity |
| title_full_unstemmed |
Q-system Cluster Algebras, Paths and Total Positivity |
| title_sort |
q-system cluster algebras, paths and total positivity |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146152 |
| citation_txt |
Q-system Cluster Algebras, Paths and Total Positivity / P. di Francesco, R. Kedem // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 28 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT difranceskop qsystemclusteralgebraspathsandtotalpositivity AT kedemr qsystemclusteralgebraspathsandtotalpositivity |
| first_indexed |
2023-05-20T17:23:58Z |
| last_indexed |
2023-05-20T17:23:58Z |
| _version_ |
1796153209113280512 |