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Dihedral solutions of the set theoretical Yang-Baxter equation
Alex W. Nowak, Anna Zamojska-Dzienio
We introduce the notion of a \emph{braided dihedral set} (BDS) to describe set-theoretical solutions of the Yang-Baxter equation (YBE) that furnish representations of the infinite…
Distributive biracks and solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We investigate a class of non-involutive solutions of the Yang-Baxter equation which generalize self-distributive (derived) solutions. In particular, we study generalized multiperm…
The construction of multipermutation solutions of the Yang-Baxter equation of level 2
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We study involutive set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2. These solutions happen to fall into two classes -- distributive ones and non-di…