21 citations · 80 across the 62 of their papers we have counts for
7 papers · 1 filter
Black-white polynomials of graphs and generating functions
Kenneth Goodenough, Paul E. Gunnells
Let G be a graph. The black-white polynomial W_G(t) enumerates colorings of the vertices of G with two colors (black and white), where the power of t keeps track of how many white…
Hypergraph matrix models and generating functions
Paul E. Gunnells
Recently we introduced the hypergraph matrix model (HMM), a Hermitian matrix model generalizing the classical Gaussian Unitary Ensemble (GUE). In this model the Gaussians of the GU…
Generalized Catalan numbers from hypergraphs
Paul E. Gunnells
The Catalan numbers (C_n)_{n >= 0} = 1,1,2,5,14,42,... form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracke…
Exotic matrix models: the Albert algebra and the spin factor
Paul E. Gunnells
The matrix models attached to real symmetric matrices and the complex/quaternionic Hermitian matrices have been studied by many authors. These models correspond to three of the sim…
Tiered trees, weights, and q-Eulerian numbers
William Dugan, Sam Glennon, Paul E. Gunnells +1
Maxmin trees are labeled trees with the property that each vertex is either a local maximum or a local minimum. Such trees were originally introduced by Postnikov, who gave a formu…
Crystal graphs, Tokuyama's theorem, and the Gindikin--Karpelevic formula for G_2
Holley Friedlander, Louis Gaudet, Paul E. Gunnells
We conjecture a deformation of the Weyl character formula for type G_2 in the spirit of Tokuyama's formula for type A. Using our conjecture we prove a combinatorial version of the…