Matrix integrals and generating functions for enumerating rooted hypermaps by vertices, edges and faces for a given number of darts

Abstract

A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of bipartite quantum systems. Direct evaluation of these generating functions is then demonstrated through the enumeration of all rooted hypermaps with up to 13 darts.

20 pages, 3 figures

References in corpus (2)

• Divergence of Lubkin's series for a quantum subsystem's mean entropy
• Matrix integrals and generating functions for permutations and one-face rooted hypermaps