Explicit enumeration and large-valence asymptotics of even-valent maps

Roozbeh Gharakhloo, Tomas Lasic Latimer

Let ${\mathcal{N}}_g(2\nu ,j)$ denote the number of connected labelled $2\nu$-valent maps of genus $g$ with $j$ vertices. Explicit bivariate formulae for ${\mathcal{N}}_g(2\nu ,j)$ have been a…