On quadrirational pentagon maps

2024/05/08 by Charalampos A. Evripidou, Evripidou, Charalampos, Pavlos Kassotakis +3 · 2 citations
Computer Science · Engineering · Mathematics · #Digital Image Processing Techniques #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2405.04945

openalex publication_date 2024/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

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.

Cited by

• Constructing solutions of simplex equations from polygon equations
• Associative Pentagon Algebras

Related

• Set-theoretical solutions to the pentagon equation: a survey
• Set-theoretical solutions of the Yang-Baxter and pentagon equations on\n semigroups
• Set-theoretical solutions of the pentagon equation on groups
• Bijective solutions to the Pentagon Equation
• Pentagon relation and Biedenharn-Elliott identity