Matrix integrals and generating functions for permutations and one-face rooted hypermaps

Jacob P. Dyer

Published 2014-07-29, updated 2015-01-27Version 2

Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum system. A recursion relation for these generating functions is also found. The method for computing similar generating functions for two-face rooted hypermaps by number of vertices and edges is outlined.