The Map Asymptotics Constant $t_g$

Edward A. Bender, Zhicheng Gao, L. Bruce Richmond


The constant $t_g$ appears in the asymptotic formulas for a variety of rooted maps on the orientable surface of genus $g$. Heretofore, studying this constant has been difficult. A new recursion derived by Goulden and Jackson for rooted cubic maps provides a much simpler recursion for $t_g$ that leads to estimates for its asymptotics.

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