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

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Journal Electronic Journal of Combinatorics
Gao, Z. (2010). A formula for the bivariate map asymptotics constants in terms of the univariate map asymptotics constants. Electronic Journal of Combinatorics, 17(1).