A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type

被引：0
作者：
Gregg Musiker
机构：
[1] Massachusetts Institute of Technology,Department of Mathematics
来源：
Annals of Combinatorics | 2011年 / 15卷
关键词：
05E15; 16S99; cluster algebras; classical type; perfect matchings; laurentness;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster algebras of finite type with bipartite seed. In particular, we provide a family of graphs such that a weighted enumeration of their perfect matchings encodes the numerator of the associated Laurent polynomial while decompositions of the graphs correspond to the denominator. This complements recent work by Schiffler and Carroll-Price for a cluster expansion formula for the An case while providing a novel interpretation for the Bn, Cn, and Dn cases.
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页码：147 / 184
页数：37
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[33]   A~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{A}$$\end{document} and D~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{D}$$\end{document} type cluster algebras: triangulated surfaces and friezes [J].
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