Combinatorics of X-variables in finite type cluster algebras

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:165

Article

Sherman-Bennett, Melissa¹ 

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

关键词: Cluster algebra;    Coefficients;    Finite type;   

DOI  :  10.1016/j.jcta.2019.02.007

来源: Elsevier

【 摘 要 】

We compute the number of X-variables (also called coefficients) of a cluster algebra of finite type when the underlying semifield is the universal semifield. For classical types, these numbers arise from a bijection between coefficients and quadrilaterals (with a choice of diagonal) appearing in triangulations of certain marked surfaces. We conjecture that similar results hold for cluster algebras from arbitrary marked surfaces, and obtain corollaries regarding the structure of finite type cluster algebras of geometric type. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free