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arXiv · 1409.8177

A Combinatorial Formula for Certain Elements of Upper Cluster Algebras

Kyungyong Lee·Li Li·Matthew R. Mills
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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.

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Kyungyong Lee, Li Li, Matthew R. Mills. 2014-09-29. A Combinatorial Formula for Certain Elements of Upper Cluster Algebras. https://doi.org/10.3842/sigma.2015.049

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