Rectangular Matrix Models and Combinatorics of Colored Graphs

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.

42 pages, 11 figures, tex, harvmac, epsf

References in corpus (1)

• Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions

Cited by in corpus (34)

• Critical behavior of colored tensor models in the large N limit
• Liouville Field Theory -- A decade after the revolution
• Colored Tensor Models - a Review
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Three-dimensional N=6 SCFT's and their membrane dynamics
• A generalization of the Virasoro algebra to arbitrary dimensions
• Instantons and Merons in Matrix Models
• Unitary and Complex Matrix Models as 1-d Type 0 Strings
• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• Ward identities and combinatorics of rainbow tensor models
• The Double Scaling Limit in Arbitrary Dimensions: A Toy Model
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Octagons I: Combinatorics and Non-Planar Resummations
• A matrix model for a quantum hall droplet with manifest particle-hole symmetry
• Asymptotic corrections to the eigenvalue density of the GUE and LUE
• Liouville theory and Matrix models: A Wheeler DeWitt perspective
• Topological recursion for irregular spectral curves
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• Topological B-Model, Matrix Models, $\hat{c}=1$ Strings and Quiver Gauge Theories
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• A string field theoretical description of (p,q) minimal superstrings
• Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity
• Linear Differential Equations for the Resolvents of the Classical Matrix Ensembles
• A random matrix model with non-pairwise contracted indices
• Surgery in colored tensor models
• The Conformal Limit of the 0A Matrix Model and String Theory on AdS(2)
• Notes on D-branes and dualities in (p,q) minimal superstring theory
• Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations
• Tensor models with generalized melonic interactions
• A Diagrammatic Equation for Oriented Planar Graphs
• Tensor Field Theories: Renormalization and Random Geometry
• Fatgraph expansion for noncritical superstrings
• $q$-Pearson pair and moments in $q$-deformed ensembles