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Mosc. Math. J., 2017, Volume 17, Number 4, Pages 601–633 (Mi mmj650)  

This article is cited in 1 scientific paper (total in 1 paper)

Classical Hurwitz numbers and related combinatorics

Boris Dubrovina, Di Yangb, Don Zagierb

a SISSA, via Bonomea 265, Trieste 34136, Italy
b Max-Planck-Institut für Mathematik, Vivatsgasse 7, Bonn 53111, Germany

Abstract: We give a polynomial-time algorithm of computing the classical Hurwitz numbers $H_{g,d}$, which were defined by Hurwitz 125 years ago. We show that the generating series of $H_{g,d}$ for any fixed $g\geq2$ lives in a certain subring of the ring of formal power series that we call the Lambert ring. We then define some analogous numbers appearing in enumerations of graphs, ribbon graphs, and in the intersection theory on moduli spaces of algebraic curves, such that their generating series belong to the same Lambert ring. Several asymptotics of these numbers (for large $g$ or for large $d$) are obtained.

Key words and phrases: Hurwitz numbers, Lambert ring, Pandharipande's equation, enumerative geometry.

DOI: https://doi.org/10.17323/1609-4514-2017-17-4-601-633

Full text: http://www.mathjournals.org/.../2017-017-004-003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 14N10; Secondary 16T30, 53D45, 05A15
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Citation: Boris Dubrovin, Di Yang, Don Zagier, “Classical Hurwitz numbers and related combinatorics”, Mosc. Math. J., 17:4 (2017), 601–633

Citation in format AMSBIB
\Bibitem{DubYanZag17}
\by Boris~Dubrovin, Di~Yang, Don~Zagier
\paper Classical Hurwitz numbers and related combinatorics
\jour Mosc. Math.~J.
\yr 2017
\vol 17
\issue 4
\pages 601--633
\mathnet{http://mi.mathnet.ru/mmj650}
\crossref{https://doi.org/10.17323/1609-4514-2017-17-4-601-633}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000416897600003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dubrovin B. Yang D., “On Cubic Hodge Integrals and Random Matrices”, Commun. Number Theory Phys., 11:2 (2017), 311–336  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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