A Combinatorial Formula for Certain Elements of Upper Cluster Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Lee, K., Li, L., Mills, M.R.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147117
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Combinatorial Formula for Certain Elements of Upper Cluster Algebras / K. Lee, L. Li, M.R. Mills // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 16 назв. — англ.

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 ra...