A Monodromy Graph Approach to the Piecewise Polynomiality of Simple, Monotone and Grothendieck Dessins d’enfants Double Hurwitz Numbers
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DOI: 10.1007/s00373-019-02030-5
Abstract: Hurwitz numbers count genus g, degree d covers of the complex projective line with fixed branched locus and fixed ramification data. An equivalent description is given by factorisations in the symmetric group. Simple double Hurwitz… read more here.
Keywords: simple monotone; grothendieck dessins; double hurwitz; hurwitz numbers ... See more keywords
Weighted Hurwitz numbers and topological recursion: An overview
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DOI: 10.1063/1.5013201
Abstract: Multiparametric families of hypergeometric $\tau$-functions of KP or Toda type serve as generating functions for weighted Hurwitz numbers, providing weighted enumerations of branched covers of the Riemann sphere. A graphical interpretation of the weighting is… read more here.
Keywords: hurwitz numbers; topological recursion; tau function; weighted hurwitz ... See more keywords
Connected (n, m)-point functions of diagonal 2-BKP tau-functions and spin double Hurwitz numbers
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DOI: 10.1063/5.0136839
Abstract: We derive an explicit formula for connected ( n, m)-point functions associated with an arbitrary diagonal tau-function of the 2-BKP hierarchy using the computation of neutral fermions and boson–fermion correspondence of type B and then… read more here.
Keywords: connected point; spin double; point functions; hurwitz numbers ... See more keywords