The Map Asymptotics Constant $t_g

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 lead...

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Published in:The Electronic journal of combinatorics 2008-03, Vol.15 (1)
Main Authors: Bender, Edward A., Gao, Zhicheng, Richmond, L. Bruce
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Language:English
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Gao, Zhicheng
Richmond, L. Bruce
description 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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