Toric Mutations in the dP2 Quiver and Subgraphs of the dP2 Brane Tiling

被引：0
|
作者：
Gao, Yibo [1 ]
Li, Zhaoqi [2 ]
Thuy-Duong Vuong [1 ]
Yang, Lisa [1 ]
机构：
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Univ Washington, Dept Stat, Seattle, WA 98195 USA
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2019年 / 26卷 / 02期
关键词：
CLUSTER ALGEBRAS; MATCHINGS; FORMULA;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Brane tilings are infinite, bipartite, periodic, planar graphs that are dual to quivers. In this paper, we study the del Pezzo 2 (dP(2)) quiver and its associated brane tiling which arise in theoretical physics. Specifically, we prove explicit formulas for all cluster variables generated by toric mutation sequences of the dP(2) quiver. Moreover, we associate a subgraph of the dP(2) brane tiling to each toric cluster variable such that the sum of weighted perfect matchings of the subgraph equals the Laurent polynomial of the cluster variable.
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页数：46
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