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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Rationality in map and hypermap enumeration by genus

Authors: P. Zograf and M. Kazarian
Translated by: P. Zograf
Original publication: Algebra i Analiz, tom 29 (2017), nomer 3.
Journal: St. Petersburg Math. J. 29 (2018), 439-445
MSC (2010): Primary 05C30, 37K10
Published electronically: March 30, 2018
MathSciNet review: 3708857
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Abstract: Generating functions for a fixed genus map and hypermap enumeration become rational after a simple explicit change of variables. Their numerators are polynomials with integral coefficients that obey a differential recursion, and the denominators are products of powers of explicit linear functions.

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Additional Information

P. Zograf
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia; Chebyshev Laboratory, St. Petersburg State University, 14th Line V.O. 29B, St. Petersburg 199178, Russia

M. Kazarian
Affiliation: Steklov Mathematical Institute, Gubkin St. 8, Moscow 119991, Russia; Department of Mathematics, National Research University Higher School of Economics, Usacheva Str. 6, Moscow 119048 Russia

Keywords: Enumeration of maps (ribbon graphs), enumeration of hypermaps (Grothendieck's ``dessins d'enfants'')
Received by editor(s): November 10, 2016
Published electronically: March 30, 2018
Additional Notes: Supported by the Russian Science Foundation: Theorem 1 by grant no. 14-21-00035, and Theorem 2 by grant no. 16-11-10316.
Article copyright: © Copyright 2018 American Mathematical Society