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 c...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2016
Hauptverfasser: Goulden, I.P., Guay-Paquet, M., Novak, J.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2016
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/147740
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers / I.P. Goulden, M. Guay-Paquet, J. Novak // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 22 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung: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.
ISSN:1815-0659