Perfect matchings and cluster algebras of classical type

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster algebras of finite type. 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 A n case while providing a novel interpretation for the B n, C n, and D n cases.

Original languageEnglish (US)
Title of host publicationFPSAC'08 - 20th International Conference on Formal Power Series and Algebraic Combinatorics
Pages435-446
Number of pages12
StatePublished - Dec 1 2008
Event20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile
Duration: Jun 23 2008Jun 27 2008

Other

Other20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
CountryChile
CityValparaiso
Period6/23/086/27/08

Keywords

  • Classical type
  • Cluster algebras
  • Laurentness
  • Perfect matchings
  • Positivity

Fingerprint Dive into the research topics of 'Perfect matchings and cluster algebras of classical type'. Together they form a unique fingerprint.

Cite this