24 citations · 62 across the 12 of their papers we have counts for
20 papers
Retracts of degenerate solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska
Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct defi…
Indecomposable non-degenerate 2-permutational solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska
We present a complete characterization of all indecomposable non-degenerate, not necessarily involutive, solutions of the Yang-Baxter equation of multipermutation level~2. We show…
Associative Pentagon Algebras
Marzia Mazzotta, Agata Pilitowska
A set-theoretic solution to the Pentagon Equation can be described as a \emph{pentagon} algebra such that is a semigroup and the operations …
Non-involutive solutions of the Yang-Baxter equation of multipermutation level 2
Jan Hora, Premysl Jedlicka, Agata Pilitowska
We study non-degenerate set-theoretic solutions of the Yang-Baxter equation of multipermutation level 2 which are not 2-reductive. We describe an effective way of constructing such…
Diagonals of solutions of the Yang-Baxter equation
Premysl Jedlicka, Agata Pilitowska
We study the diagonal mappings in non-involutive set-theoretic solutions of the Yang-Baxter equation. We show that, for non-degenerate solutions, they are commuting bijections. Thi…
Skew left braces and 2-reductive solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska
We study 2-reductive non-involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation. We give a combinatorial construction of any such solution of any (even infin…
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group
Přemysl Jedlička, Agata Pilitowska
We give a complete characterization of all indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level~2. In the first step we present a construction…
Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation
Přemysl Jedlička, Agata Pilitowska, Anna Zamojska-Dzienio
We study indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with cyclic permutation groups (cocyclic solutions). In particular, we show that there is no…
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…
Knot-theoretic ternary groups
Maciej Niebrzydowski, Agata Pilitowska, Anna Zamojska-Dzienio
We describe various properties and give several characterizations of ternary groups satisfying two axioms derived from the third Reidemeister move in knot theory. Using special att…
Subquandles of affine quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their d…
Free medial quandles
Premysl Jedlicka, Agata Pilitowska, Anna Zamojska-Dzienio
This paper brings the construction of free medial quandles as well as free -symmetric medial quandles and free -reductive medial quandles.
Subdirectly irreducible medial quandles
Premysl Jedlicka, Agata Pilitowska, Anna Zamojska-Dzienio
We describe all subdirectly irreducible medial quandles. We show that they fall within one of four disjoint classes. In particular, in the finite case they are either connected (an…
The structure of medial quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
Medial quandles are represented using a heterogeneous affine structure. As a consequence, we obtain numerous structural properties, including enumeration of isomorphism classes of…
Closure operators on algebras
Agata Pilitowska, Anna Zamojska-Dzienio
We study connections between closure operators on an algebra $(A,\Om)$ and congruences on the extended power algebra defined on the same algebra. We use these connections to give a…