Rationality in map and hypermap enumeration by genus
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P. Zograf and M. Kazarian
Translated by: P. Zograf - St. Petersburg Math. J. 29 (2018), 439-445
- DOI: https://doi.org/10.1090/spmj/1501
- Published electronically: March 30, 2018
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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.References
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Bibliographic 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
- Email: zograf@pdmi.ras.ru
- 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
- Email: kazarian@mccme.ru
- 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.
- © Copyright 2018 American Mathematical Society
- Journal: St. Petersburg Math. J. 29 (2018), 439-445
- MSC (2010): Primary 05C30, 37K10
- DOI: https://doi.org/10.1090/spmj/1501
- MathSciNet review: 3708857