Abstract
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 ) ↦ ( 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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