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Classical 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.
Symmetric polynomials and the center of the symmetric group ring
A.-A. A. Jucys · 1974
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Moduli of curves
J. Harris and I. Morrison · 1998
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Hurwitz numbers and intersections on moduli spaces of curves
T. Ekedahl, S. Lando, M. Shapiro, and A. Vainshtein · 2001
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The colored Jones function is
S. Garoufalidis and T. T. Q. Lê · 2005
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B. Eynard and N. Orantin · 2007
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Weil–Petersson volume of moduli spaces, Mirzakhani’s recursion and matrix models
B. Eynard and N. Orantin · 2007
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V. Bouchard and M. Mariño · 2008
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V. Bouchard, A. Klemm, M. Mariño, and S. Pasquetti · 2009
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R. Dijkgraaf, H. Fuji, and M. Manabe · 2011
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B. Eynard · 2011
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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
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P. Norbury and N. Scott · 2011
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G. Borot and B. Eynard · 2012
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Orbifold Hurwitz numbers and Eynard–Orantin invariants
N. Do, O. Leigh, and P. Norbury · 2012
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Quantum curves for the enumeration of ribbon graphs and hypermaps
N. Do and D. Manescu · 2013
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The spectral curve of the Eynard-Orantin recursion via the Laplace transform
O. Dumitrescu, M. Mulase, B. Safnuk, and A. Sorkin · 2013
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Quantum spectral curve for the Gromov–Witten theory of the complex projective line
P. Dunin-Barkowski, M. Mulase, P. Norbury, A. Popolitov, and S. Shadrin · 2013
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All genus open-closed mirror symmetry for affine toric Calabi–Yau 3-orbifolds
B. Fang, C.-C. M. Liu, and Z. Zong · 2013
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Monotone Hurwitz numbers in genus zero
I. P. Goulden, M. Guay-Paquet, and J. Novak · 2013
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S. Gukov and P. Sułkowski · 2012
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M. Mulase and P. Sułkowski · 2012
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J. Zhou · 2012
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J. Zhou · 2012
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Think globally, compute locally
V. Bouchard and B. Eynard · 2013
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Mirror symmetry for orbifold Hurwitz numbers
V. Bouchard, D. Hernández Serrano, X. Liu, and M. Mulase · 2013
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Polynomiality of monotone Hurwitz numbers in higher genera
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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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String and dilaton equations for counting lattice points in the moduli space of curves
P. Norbury · 2013
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Identification of the Givental formula with the spectral curve topological recursion procedure
P. Dunin-Barkowski, N. Orantin, S. Shadrin, and L. Spitz · 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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