Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations
We derive series representations for the tau functions of the q-Painlevé V, III₁, III₂, and III₃ equations, as degenerations of the tau functions of the q-Painlevé VI equation in [Jimbo M., Nagoya H., Sakai H., J. Integrable Syst. 2 (2017), xyx009, 27 pages]. Our tau functions are expressed in terms...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
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| Sprache: | English |
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Інститут математики НАН України
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| Zitieren: | Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations / Y. Matsuhira, H. Nagoya // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 28 назв. — англ. |
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Matsuhira, Y. Nagoya, H. 2025-12-04T13:00:56Z 2019 Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations / Y. Matsuhira, H. Nagoya // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 39A13; 33E17; 05A30 arXiv: 1811.03285 https://nasplib.isofts.kiev.ua/handle/123456789/210221 https://doi.org/10.3842/SIGMA.2019.074 We derive series representations for the tau functions of the q-Painlevé V, III₁, III₂, and III₃ equations, as degenerations of the tau functions of the q-Painlevé VI equation in [Jimbo M., Nagoya H., Sakai H., J. Integrable Syst. 2 (2017), xyx009, 27 pages]. Our tau functions are expressed in terms of q-Nekrasov functions. Thus, our series representations for the tau functions have explicit combinatorial structures. We show that general solutions to the q-Painlevé V, III₁, III₂, and III₃ equations are written by our tau functions. We also prove that our tau functions for the q-Painlevé III₁, III₂, and III₃ equations satisfy the three-term bilinear equations for them. This work is partially supported by JSPS KAKENHI Grant Number JP15K17560. The authors thank the referees for their valuable suggestions and comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations |
| spellingShingle |
Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations Matsuhira, Y. Nagoya, H. |
| title_short |
Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations |
| title_full |
Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations |
| title_fullStr |
Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations |
| title_full_unstemmed |
Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations |
| title_sort |
combinatorial expressions for the tau functions of q-painlevé v and iii equations |
| author |
Matsuhira, Y. Nagoya, H. |
| author_facet |
Matsuhira, Y. Nagoya, H. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We derive series representations for the tau functions of the q-Painlevé V, III₁, III₂, and III₃ equations, as degenerations of the tau functions of the q-Painlevé VI equation in [Jimbo M., Nagoya H., Sakai H., J. Integrable Syst. 2 (2017), xyx009, 27 pages]. Our tau functions are expressed in terms of q-Nekrasov functions. Thus, our series representations for the tau functions have explicit combinatorial structures. We show that general solutions to the q-Painlevé V, III₁, III₂, and III₃ equations are written by our tau functions. We also prove that our tau functions for the q-Painlevé III₁, III₂, and III₃ equations satisfy the three-term bilinear equations for them.
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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210221 |
| citation_txt |
Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations / Y. Matsuhira, H. Nagoya // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 28 назв. — англ. |
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AT matsuhiray combinatorialexpressionsforthetaufunctionsofqpainlevevandiiiequations AT nagoyah combinatorialexpressionsforthetaufunctionsofqpainlevevandiiiequations |
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2025-12-07T21:24:47Z |
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2025-12-07T21:24:47Z |
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1850886259131547648 |