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Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types.
B. Eynard and N. Orantin, Invariants of algebraic curves and topological expansion , Commun. Number Theory Phys. 1
1931
Earlier work this paper cites.
Harish-Chandra, Differential operators on a semisimple Lie algebra , Amer. J. Math. 79
1957
Earlier work this paper cites.
A.-A. A. Jucys, Symmetric polynomials and the center of the symmetric group ring , Rep. Mathematical Phys. 5
1974
Earlier work this paper cites.
C. Itzykson and J. B. Zuber, The planar approximation. II , J. Math. Phys. 21
1980
Earlier work this paper cites.
I. P. Goulden and David M. Jackson, Combinatorial enumeration , Dover Publications Inc., Mineola, NY, 2004, ISBN 0-486-43597-0, With a foreword by Gian-Carlo Rota, Reprint of the 1983 original
1983
Earlier work this paper cites.
Edward Witten, Two-dimensional gravity and intersection theory on moduli space , Surveys in differential geometry (Cambridge, MA, 1990), Lehigh Univ., Bethlehem, PA, 1991, pp. 243–310
1991
Earlier work this paper cites.
Maxim Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function , Comm. Math. Phys. 147
1992
Earlier work this paper cites.
I. G. Macdonald, Symmetric functions and Hall polynomials , second ed., Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1995, ISBN 0-19-853489-2, With contributions by A. Zelevinsky, Oxford Science Publications
1995
Earlier work this paper cites.
A. Zvonkin, Matrix integrals and map enumeration: an accessible introduction , Math. Comput. Modelling 26
1995
Earlier work this paper cites.
Andrei Okounkov and Anatoly Vershik, A new approach to representation theory of symmetric groups , Selecta Math. (N.S.) 2
1996
Earlier work this paper cites.
Volker Strehl, Minimal transitive products of transpositions—the reconstruction of a proof of A. Hurwitz , Sém. Lothar. Combin. 37
1996
Cited alongside, same era.
I. P. Goulden and D. M. Jackson, Transitive factorisations into transpositions and holomorphic mappings on the sphere , Proc. Amer. Math. Soc. 125
1997
Cited alongside, same era.
Mireille Bousquet-Mélou and Gilles Schaeffer, Enumeration of planar constellations , Adv. in Appl. Math. 24
1999
Cited alongside, same era.
I. P. Goulden, D. M. Jackson, and A. Vainshtein, The number of ramified coverings of the sphere by the torus and surfaces of higher genera , Ann. Comb. 4
2000
Cited alongside, same era.
Torsten Ekedahl, Sergei Lando, Michael Shapiro, and Alek Vainshtein, Hurwitz numbers and intersections on moduli spaces of curves , Invent. Math. 146
2001
Cited alongside, same era.
M. E. Kazarian and S. K. Lando, An algebro-geometric proof of Witten’s conjecture , J. Amer. Math. Soc. 20
2007
Later among the works it cites.
Vincent Bouchard and Marcos Mariño, Hurwitz numbers, matrix models and enumerative geometry , From Hodge theory to integrability and TQFT tt*-geometry, Proc. Sympos. Pure Math., vol. 78, Amer. Math. Soc., Providence, RI, 2008, pp. 263–283
2008
Later among the works it cites.
The Sage-Combinat community, Sage-Combinat: enhancing Sage as a toolbox for computer exploration in algebraic combinatorics , 2008, http://combinat.sagemath.org
2008
Later among the works it cites.
2009
Later among the works it cites.
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P. Zinn-Justin, HCIZ integral and 2D Toda lattice hierarchy , Nuclear Phys. B 634
2002
Cited alongside, same era.
P. Zinn-Justin and J.-B. Zuber, On some integrals over the U ( N ) {\rm U}(N) unitary group and their large N N limit , J. Phys. A 36
2003
Cited alongside, same era.
Sergei K. Lando and Alexander K. Zvonkin, Graphs on surfaces and their applications , Encyclopaedia of Mathematical Sciences, vol. 141, Springer-Verlag, Berlin, 2004, ISBN 3-540-00203-0, With an appendix by Don B. Zagier, Low-Dimensional Topology, II
2004
Cited alongside, same era.
Daniele A. Gewurz and Francesca Merola, Some factorisations counted by Catalan numbers , European J. Combin. 27
2005
Cited alongside, same era.
I. P. Goulden, Mathieu Guay-Paquet, and Jonathan Novak, Polynomiality of monotone Hurwitz numbers in higher genera , in preparation
Cited in the paper.
A. Hurwitz, Über Riemann’sche Flächen mit gegebenen Verzweigungspunkten , Mathematische Annalen 39
Cited in the paper.
A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers, and matrix models , Algebraic geometry—Seattle 2005. Part 1, Proc. Sympos. Pure Math., vol. 80, Amer. Math. Soc., Providence, RI, 2009, pp. 325–414
2009
Later among the works it cites.
2010
Later among the works it cites.
W. A. Stein et al., Sage mathematics software (version 4.6) , 2010, URL http://www.sagemath.org
2010
Later among the works it cites.
2011
Later among the works it cites.