24 citations · 65 across the 15 of their papers we have counts for
21 papers
On the intrinsic geometry of polyhedra: Convex polygon coordinates
Anna B. Romanowska, Jonathan D. H. Smith, Anna Zamojska-Dzienio
There is a very extensive literature dealing with convex polytopes from the standpoints of combinatorics and numerical analysis. By contrast, the current paper adopts an alternativ…
In Search of Homology for Quasigroups of Bol-Moufang Type
Anthony Christiana, Ben Clingenpeel, Huizheng Guo +3
We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define…
Conjecture on Maximal Sublattices of Finite Semidistributive Lattices and Beyond
K. Adaricheva, A. Mata, S. Silberger +1
We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be…
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…
Barycentric algebras -- convexity and order
Anna Zamojska-Dzienio
This is the abstract of a series of lectures given during the XIIIth School on Geometry and Physics, Bialystok (Poland), in July 2024. In this minicourse, we first examine the alge…
Partitions of unity and barycentric algebras
Anna Zamojska-Dzienio
Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. T…
From affine to barycentric coordinates in polytopes
Anna B. Romanowska, Jonathan D. H. Smith, Anna Zamojska-Dzienio
Each point of a simplex is expressed as a unique convex combination of the vertices. The coefficients in the combination are the barycentric coordinates of the point. For each poin…
The inverse problem of convex polygon coordinates
A. B. Romanowska, J. D. H. Smith, A. Zamojska-Dzienio
Each convex combination of extreme points of a compact convex set represents a certain point of the convex set. Barycentric coordinates provide solutions to the inverse problem of…
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…