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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 040, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.040 (Mi sigma1122) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers

I. P. Gouldena, Mathieu Guay-Paquetb, Jonathan Novakc

a Department of Combinatorics and Optimization, University of Waterloo, 200 University Ave. W., Waterloo, ON, N2L 3G1 Canada
b Département de mathématiques, Université du Québec à Montréal, C.P. 8888, succ. Centre-ville, Montréal, Québec, H3C 3P8 Canada
c Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0404 USA
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DOI: https://doi.org/10.3842/SIGMA.2016.040
Abstract: 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 partial differential equations. We also prove that the mixed double Hurwitz numbers are piecewise polynomial, thereby generalizing a result of Goulden, Jackson and Vakil.
Keywords: Hurwitz numbers; Toda lattice.
Received: February 2, 2016; in final form April 13, 2016; Published online April 20, 2016
Bibliographic databases:
Document Type: Article
MSC: 05A05; 14H70
Language: English
Citation: I. P. Goulden, Mathieu Guay-Paquet, Jonathan Novak, “Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers”, SIGMA, 12 (2016), 040, 10 pp.
Citation in format AMSBIB
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\paper Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers
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\papernumber 040
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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