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 |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2016
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| 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| _version_ | 1862735422577180672 |
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| author | Goulden, I.P. Guay-Paquet, M. Novak, J. |
| author_facet | Goulden, I.P. Guay-Paquet, M. Novak, J. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T19:48:57Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147740 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:48:57Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Goulden, I.P. Guay-Paquet, M. Novak, J. 2019-02-15T18:58:52Z 2019-02-15T18:58:52Z 2016 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. 1815-0659 2010 Mathematics Subject Classification: 05A05; 14H70 DOI:10.3842/SIGMA.2016.040 https://nasplib.isofts.kiev.ua/handle/123456789/147740 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. This paper is a contribution to the Special Issue on Asymptotics and Universality in Random Matrices,
 Random Growth Processes, Integrable Systems and Statistical Physics in honor of Percy Deift and Craig Tracy.
 The full collection is available at http://www.emis.de/journals/SIGMA/Deift-Tracy.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers Article published earlier |
| spellingShingle | Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers Goulden, I.P. Guay-Paquet, M. Novak, J. |
| title | Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers |
| title_full | Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers |
| title_fullStr | Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers |
| title_full_unstemmed | Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers |
| title_short | Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers |
| title_sort | toda equations and piecewise polynomiality for mixed double hurwitz numbers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147740 |
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