Cluster Variables and Perfect Matchings of Subgraphs of the $d{P}_3$ Lattice

Abstract

We give a combinatorial intepretation of cluster variables of a specific cluster algebra under a mutation sequence of period 6, in terms of perfect matchings of subgraphs of the brane tiling dual to the quiver associated with the cluster algebra.

19 pages, 12 figures. Previously appeared at http://www.math.umn.edu/~reiner/REU/Zhang2012.pdf

References in corpus (3)

• Brane Tilings and Reflexive Polygons
• Perfect Matchings and the Octahedron Recurrence
• Cluster expansion formulas and perfect matchings

Cited by in corpus (3)

• Beyond Aztec Castles: Toric Cascades in the $d{P}_3$ Quiver
• Dungeons and Dragons: Combinatorics for the $d{P}_3$ Quiver
• A $q$-enumeration of lozenge tilings of a hexagon with three dents