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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2016 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147740 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147740 |
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irk-123456789-1477402019-02-16T01:25:16Z Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers Goulden, I.P. Guay-Paquet, M. Novak, J. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147740 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Goulden, I.P. Guay-Paquet, M. Novak, J. |
| spellingShingle |
Goulden, I.P. Guay-Paquet, M. Novak, J. Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Goulden, I.P. Guay-Paquet, M. Novak, J. |
| author_sort |
Goulden, I.P. |
| title |
Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers |
| title_short |
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_sort |
toda equations and piecewise polynomiality for mixed double hurwitz numbers |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147740 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:28:11Z |
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