A Formula for the Bivariate Map Asymptotics Constants in terms of the Univariate Map Asymptotics Constants

Abstract

The parameters $t_g$, $p_g$, $t_g(r)$ and $p_g(r)$ appear in the asymptotics for a variety of maps on surfaces and embeddable graphs. In this paper we express $t_g(r)$ in terms of $t_g$ and $p_g(r)$ in terms of $p_g$.