On quadrirational pentagon maps
Charalampos Evripidou, Pavlos Kassotakis, Anastasios Tongas

TL;DR
This paper classifies rational quadrirational solutions to the set-theoretical pentagon equation, introduces entwining solutions with partial inverses, and explores how to derive Yang-Baxter maps from these pentagon solutions.
Contribution
It provides a complete classification of rational quadrirational pentagon maps and introduces methods to generate Yang-Baxter maps from them.
Findings
Classified all quadrirational solutions to the pentagon equation.
Established a link between pentagon maps with partial inverses and entwining solutions.
Demonstrated how to derive Yang-Baxter maps from pentagon solutions.
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 where 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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Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems · Digital Image Processing Techniques
