Two approaches to Map Enumeration: Matrix Integrals and Connections to Trees

By Vivian Healey

November 13, 2012

Abstract

A map is a graph embedded in a surface. We will address two distinct approaches to counting maps of certain types. The first approach is a clever connection to matrix integrals that utilizes Feynman diagrams. The second is a set of bijections among maps, trees, and Dyke paths.