Constructing large tables of numbers of maps by orientable genus

Abstract

The Carrell-Chapuy recurrence formulas dramatically improve the efficiency of counting orientable rooted maps by genus, either by number of edges alone or by number of edges and vertices. This paper presents an implementation of these formulas with three applications: the computation of an explicit rational expression for the ordinary generating functions of rooted map numbers with a given positive genus, the construction of large tables of rooted map numbers, and the use of these tables, together with the method of A. Mednykh and R. Nedela, to count unrooted maps by genus and number of edges and vertices.