Enumeration of N-rooted maps using quantum field theory

Abstract

A one-to-one correspondence is proved between the N-rooted ribbon graphs, or maps, with e edges and the (e−N+1)-loop Feynman diagrams of a certain quantum field theory. This result is used to obtain explicit expressions and relations for the generating functions of N-rooted maps and for the numbers of N-rooted maps with a given number of edges using the path integral approach applied to the corresponding quantum field theory.