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math.QA2023
Płonka bi-magmas and the set-theoretic Yang--Baxter equation
A. L. Agore, A. Chirvasitu, G. Militaru
We introduce a new variety of non-associative algebras, called \emph{Płonka bi-magmas}, and use them to construct novel solutions to the set-theoretic Yang-Baxter (YB) equation. We…
math.QA2023
The set-theoretic Yang-Baxter equation, Kimura semigroups and functional graphs
A. L. Agore, A. Chirvasitu, G. Militaru
We prove that the category of solutions of the set-theoretic Yang-Baxter equation of Frobenius-Separability (FS) type is equivalent to the category of pointed Kimura semigroups. As…