Polynomiality of monotone Hurwitz numbers in higher genera

DOI10.1016/j.aim.2013.01.012zbMath1285.05008arXiv1210.3415OpenAlexW2006085047MaRDI QIDQ387874

Jonathan Novak, Mathieu Guay-Paquet, Ian P. Goulden

Publication date: 17 December 2013

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.3415

zbMATH Keywords

generating functionmonotone Hurwitz numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Random matrices (algebraic aspects) (15B52) Coverings in algebraic geometry (14E20)

Related Items (19)

Toda equations and piecewise polynomiality for mixed double Hurwitz numbers ⋮ Combinatorial solutions to integrable hierarchies ⋮ Cut-and-join equation for monotone Hurwitz numbers revisited ⋮ Generating functions of bipartite maps on orientable surfaces ⋮ Ramifications of Hurwitz theory, KP integrability and quantum curves ⋮ Topological recursion for monotone orbifold Hurwitz numbers: a proof of the Do-Karev conjecture ⋮ Topological recursion and a quantum curve for monotone Hurwitz numbers ⋮ Monotone Hurwitz numbers and the HCIZ integral ⋮ Double Hurwitz numbers: polynomiality, topological recursion and intersection theory ⋮ Monotone orbifold Hurwitz numbers ⋮ Moment methods on compact groups: Weingarten calculus and its applications ⋮ Asymptotics for real monotone double Hurwitz numbers ⋮ Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion ⋮ Contents of partitions and the combinatorics of permutation factorizations in genus $0$ ⋮ On the convergence of monotone Hurwitz generating functions ⋮ Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants ⋮ Generalisations of the Harer-Zagier recursion for 1-point functions ⋮ Integer moments of complex Wishart matrices and Hurwitz numbers ⋮ Combinatorial and algebraic enumeration: a survey of the work of Ian P. Goulden and David M. Jackson

Uses Software

• SageMath
• Sage-Combinat

Cites Work

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• KP hierarchy for Hodge integrals
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• Hurwitz numbers and intersections on moduli spaces of curves.
• A proof of a conjecture for the number of ramified coverings of the sphere by the torus
• The number of ramified coverings of the sphere by the double torus, and a general form for higher genera
• The number of ramified coverings of the sphere by the torus and surfaces of higher genera
• Genus $0$ and $1$ Hurwitz numbers: Recursions, formulas, and graph-theoretic interpretations
• The Gromov-Witten Potential of A Point, Hurwitz Numbers, and Hodge Integrals
• Monotone Hurwitz Numbers in Genus Zero
• An algebro-geometric proof of Witten’s conjecture
• Generating functions for weighted Hurwitz numbers
• Transitive factorisations into transpositions and holomorphic mappings on the sphere

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