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TROPICAL OPEN HURWITZ NUMBERS
"... Abstract. We give a tropical interpretation of Hurwitz numbers extending the one discovered in [CJM]. In addition we treat a generalization of Hurwitz numbers for surfaces with boundary which we call open Hurwitz numbers. Hurwitz numbers are defined as the (weighted) number of ramified coverings of ..."
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Abstract. We give a tropical interpretation of Hurwitz numbers extending the one discovered in [CJM]. In addition we treat a generalization of Hurwitz numbers for surfaces with boundary which we call open Hurwitz numbers. Hurwitz numbers are defined as the (weighted) number of ramified coverings
Tropical Hurwitz numbers
"... Abstract. Hurwitz numbers count genus g, degree d covers of P 1 with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piecewise linear objects called tropical curves. This paper develops a ..."
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Cited by 14 (4 self)
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Abstract. Hurwitz numbers count genus g, degree d covers of P 1 with fixed branch locus. This equals the degree of a natural branch map defined on the Hurwitz space. In tropical geometry, algebraic curves are replaced by certain piecewise linear objects called tropical curves. This paper develops
pADIC HURWITZ NUMBERS
, 806
"... Abstract. We introduce stable tropical curves, and use these to count covers of the padic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers. 1. ..."
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Abstract. We introduce stable tropical curves, and use these to count covers of the padic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers. 1.
equations for Hurwitz numbers
"... We consider ramified coverings of P 1 with arbitrary ramification type over 0, ∞ ∈ P 1 and simple ramifications elsewhere and prove that the generating function for the numbers of such coverings is a τfunction for the Toda lattice hierarchy of Ueno and Takasaki. ..."
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Cited by 64 (3 self)
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We consider ramified coverings of P 1 with arbitrary ramification type over 0, ∞ ∈ P 1 and simple ramifications elsewhere and prove that the generating function for the numbers of such coverings is a τfunction for the Toda lattice hierarchy of Ueno and Takasaki.
MONOTONE HURWITZ NUMBERS IN GENUS ZERO
"... Abstract. 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. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the H ..."
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Cited by 2 (1 self)
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Abstract. 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. Monotone Hurwitz numbers count a restricted subset of the branched covers counted
Towards the geometry of double Hurwitz numbers
 Advances Math
"... ABSTRACT. Double Hurwitz numbers count branched covers of CP 1 with fixed branch points, with simple branching required over all but two points 0 and ∞, and the branching over 0 and ∞ points specified by partitions of the degree (with m and n parts respectively). Single Hurwitz numbers (or more usua ..."
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Cited by 44 (6 self)
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ABSTRACT. Double Hurwitz numbers count branched covers of CP 1 with fixed branch points, with simple branching required over all but two points 0 and ∞, and the branching over 0 and ∞ points specified by partitions of the degree (with m and n parts respectively). Single Hurwitz numbers (or more
MIRROR SYMMETRY FOR ORBIFOLD HURWITZ NUMBERS
"... Abstract. We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin with spectral curve given by the rLambert curve. We ..."
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Cited by 9 (5 self)
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Abstract. We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin with spectral curve given by the rLambert curve
Bijections for simple and double Hurwitz numbers
"... Abstract. We give a bijective proof of Hurwitz formula for the number of simple branched coverings of the sphere by itself. Our approach extends to double Hurwitz numbers and yields new properties for them. In particular we prove for double Hurwitz numbers a conjecture of Kazarian and Zvonkine, and ..."
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Abstract. We give a bijective proof of Hurwitz formula for the number of simple branched coverings of the sphere by itself. Our approach extends to double Hurwitz numbers and yields new properties for them. In particular we prove for double Hurwitz numbers a conjecture of Kazarian and Zvonkine
Spin Hurwitz numbers and the Gromov–Witten
"... The classical Hurwitz numbers which count coverings of a complex curve have an analog when the curve is endowed with a theta characteristic. These “spin Hurwitz numbers, ” recently studied by Eskin, Okounkov and Pandharipande, are interesting in their own right. By the authors ’ previous work, they ..."
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The classical Hurwitz numbers which count coverings of a complex curve have an analog when the curve is endowed with a theta characteristic. These “spin Hurwitz numbers, ” recently studied by Eskin, Okounkov and Pandharipande, are interesting in their own right. By the authors ’ previous work
Results 1  10
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17,166