7 papers
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We present a construction of all finite indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level at most 2 with abelian permutation group. As a c…
Semilattice ordered algebras with constants
Agata Pilitowska, Anna Zamojska-Dzienio
We continue our studies on semilattice ordered algebras. This time we accept constants in the type of algebras. We investigate identities satisfied by such algebras and describe th…
Knot-theoretic flocks
Maciej Niebrzydowski, Agata Pilitowska, Anna Zamojska-Dzienio
We characterize the para-associative ternary quasigroups (flocks) applicable to knot theory, and show which of these structures are isomorphic. We enumerate them up to order 64. We…
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…
The retraction relation for biracks
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
In {\it Set-theoretical solutions to the quantum Yang-Baxter equation} (Duke Math. J. {\bf 100} (1999), 169--209), Etingof, Schedler and Soloviev introduced, for each non-degenerat…