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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 049, 24 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.049 (Mi sigma1030) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A Combinatorial Formula for Certain Elements of Upper Cluster Algebras

Kyungyong Leeab, Li Lic, Matthew R. Millsa

a Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
b Korea Institute for Advanced Study, Seoul, Republic of Korea 130-722
c Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
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DOI: https://doi.org/10.3842/SIGMA.2015.049
Abstract: We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra.
Keywords: cluster algebra; upper cluster algebra; Dyck path.
Received: September 30, 2014; in final form June 22, 2015; Published online June 26, 2015
Bibliographic databases:
Document Type: Article
MSC: 13F60
Language: English
Citation: Kyungyong Lee, Li Li, Matthew R. Mills, “A Combinatorial Formula for Certain Elements of Upper Cluster Algebras”, SIGMA, 11 (2015), 049, 24 pp.
Citation in format AMSBIB
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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