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arXiv · 2405.04945

On quadrirational pentagon maps

Charalampos Evripidou·Pavlos Kassotakis·Anastasios Tongas
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Abstract

We classify rational solutions of a specific type of the set theoretical version of the pentagon equation. That is, we find all quadrirational maps $R:(x,y)\mapsto (u(x,y),v(x,y)),$ where $u, v$ are two rational functions on two arguments, that serve as solutions of the pentagon equation. Furthermore, provided a pentagon map that admits a partial inverse, we obtain genuine entwining pentagon set theoretical solutions. Finally, we show how to obtain Yang-Baxter maps from entwining pentagon maps.

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Charalampos Evripidou, Pavlos Kassotakis, Anastasios Tongas. 2024-05-08. On quadrirational pentagon maps. https://arxiv.org/abs/2405.04945

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