Rectangular Matrix Models and Combinatorics of Colored Graphs

TL;DR

This paper explores how rectangular matrix models can be applied to solve combinatorial problems involving colored graphs and triangulations, with potential applications in statistical physics models on random lattices.

Contribution

It introduces novel applications of rectangular matrix models to enumerate colored graphs and triangulations, expanding their use in combinatorics and statistical physics.

Findings

Enumeration formulas for face-bicolored graphs with prescribed degrees

Methods for counting vertex-tricolored triangulations

Potential applications to statistical models on random lattices

Abstract

We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible applications to Interaction-Round-a-Face and hard-particle statistical models defined on random lattices.