Generalized string equations for double Hurwitz numbers
نویسندگان
چکیده
منابع مشابه
Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers
This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hurwitz numbers introduced recently by Goulden, Guay-Paquet and Novak. Generalizing a result of Okounkov, we prove that a certain generating series for the mixed double Hurwitz numbers solves the 2-Toda hierarchy of part...
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Hurwitz numbers count ramified genus g, degree d coverings of the projective line with fixed branch locus and fixed ramification data. Double Hurwitz numbers count such covers, where we fix two special profiles over 0 and ∞ and only simple ramification else. These objects feature interesting structural behaviour and connections to geometry. In this paper, we introduce the notion of pruned doubl...
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Abstract. In this paper, we collect a number of facts about double Hurwitz numbers, where the simple branch points are replaced by their more general analogues — completed (r + 1)-cycles. In particular, we give a geometric interpretation of these generalised Hurwitz numbers and derive a cut-and-join operator for completed (r+1)-cycles. We also prove a strong piecewise polynomiality property in ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2012
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2011.12.005