# Combinatorial Expressions for the Tau Functions of q-Painlevé V and III Equations

@article{Matsuhira2019CombinatorialEF,
title={Combinatorial Expressions for the Tau Functions of q-Painlev{\'e} V and III Equations},
author={Yuya Matsuhira and Hajime Nagoya},
journal={Symmetry, Integrability and Geometry: Methods and Applications},
year={2019}
}
• Published 8 November 2018
• Mathematics
• Symmetry, Integrability and Geometry: Methods and Applications
We derive series representations for the tau functions of the $q$-Painlev\'e V, $\mathrm{III_1}$, $\mathrm{III_2}$, and $\mathrm{III_3}$ equations, as degenerations of the tau functions of the $q$-Painlev\'e 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…
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