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In general, Hurwitz numbers count branched covers of the Riemann sphere with prescribed ramification data, or equivalently, factorisations in the symmetric group with prescribed cycle structure data.
Transitive factorisations into transpositions and holomorphic mappings on the sphere
I. P. Goulden and D. M. Jackson · 1997
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Moduli of curves
J. Harris and I. Morrison · 1998
Earlier work this paper cites.
The number of ramified coverings of the sphere by the torus and surfaces of higher genera
I. P. Goulden, D. M. Jackson, and A. Vainshtein · 2000
Earlier work this paper cites.
Hurwitz numbers and intersections on moduli spaces of curves
T. Ekedahl, S. Lando, M. Shapiro, and A. Vainshtein · 2001
Earlier work this paper cites.
Hermitian matrix model free energy: Feynman graph technique for all genera
L. Chekhov and B. Eynard · 2006
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A preliminary text on the
D. Zvonkine · 2006
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Invariants of algebraic curves and topological expansion
B. Eynard and N. Orantin · 2007
Earlier work this paper cites.
Tropical Hurwitz numbers
R. Cavalieri, P. Johnson, and H. Markwig · 2010
Cited alongside, same era.
Wall crossings for double Hurwitz numbers
R. Cavalieri, P. Johnson, and H. Markwig · 2011
Cited alongside, same era.
The Laplace transform of the cut-and-join equation and the Bouchard-Mariño conjecture on Hurwitz numbers
B. Eynard, M. Mulase, and B. Safnuk · 2011
Cited alongside, same era.
Abelian Hurwitz-Hodge integrals
P. Johnson, R. Pandharipande, and H.-H. Tseng · 2011
Cited alongside, same era.
A-polynomial, B-model, and quantization
S. Gukov and P. Sułkowski · 2012
Cited alongside, same era.
The spectral curve of the Eynard-Orantin recursion via the Laplace transform
O. Dumitrescu, M. Mulase, B. Safnuk, and A. Sorkin · 2013
Cited alongside, same era.
Polynomiality of monotone Hurwitz numbers in higher genera
I. P. Goulden, M. Guay-Paquet, and J. Novak · 2013
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The spectral curve and the Schrödinger equation of double Hurwitz numbers and higher spin structures
M. Mulase, S. Shadrin, and L. Spitz · 2013
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Mirror symmetry for orbifold Hurwitz numbers
V. Bouchard, D. Hernández Serrano, X. Liu, and M. Mulase · 2014
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Monotone Hurwitz numbers and the HCIZ integral
I. P. Goulden, M. Guay-Paquet, and J. Novak · 2014
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The combinatorics of real double Hurwitz numbers with real positive branch points
M. Guay-Paquet, H. Markwig, and J. Rau · 2015
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Tropical real Hurwitz numbers
H. Markwig and J. Rau · 2015
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Monotone Hurwitz numbers in genus zero
I. P. Goulden, M. Guay-Paquet, and J. Novak · 2013
Cited alongside, same era.
To appear
A. Alexandrov, D. Lewanski, and S. Shadrin
Cited in the paper.
Topological recursion and a quantum curve for monotone Hurwitz numbers
N. Do, A. Dyer, and D. Mathews
Cited in the paper.
Orbifold Hurwitz numbers and Eynard–Orantin invariants
N. Do, O. Leigh, and P. Norbury
Cited in the paper.
P. Dunin-Barkowski, D. Lewanski, A. Popolitov, and S. Shadrin
Cited in the paper.
Intersection numbers of spectral curves
B. Eynard
Cited in the paper.
Equivalence of ELSV and Bouchard–Mariño conjectures for
S. Shadrin, L. Spitz, and D. Zvonkine · 2015
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