RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mosc. Math. J.: Year: Volume: Issue: Page: Find

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

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
Language:

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} 

• http://mi.mathnet.ru/eng/mmj650
• http://mi.mathnet.ru/eng/mmj/v17/i4/p601

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. J. Rau, “Lower bounds and asymptotics of real double hurwitz numbers”, Math. Ann., 375:1-2 (2019), 895–915
3. Zh. Wang, J. Zhou, “A unified approach to holomorphic anomaly equations and quantum spectral curves”, J. High Energy Phys., 2019, no. 4, 135
4. B. Dubrovin, D. Yang, “On Gromov-witten Invariants of P-1”, Math. Res. Lett., 26:3 (2019), 729–748