Results 51 to 60 of about 3,309 (193)
, 2008 We characterize the set of all N-ary quasigroups of order 4: every N-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an N-ary quasigroup can be represented as a composition of K-ary and (N-K+1)-ary ...
Denis S. Krotov +2 more
core +1 more source
The structure of F-quasigroups
Journal of Algebra, 2007 24 pages. v.2 incorporates minor changes suggested by the referee.
Kepka, Tomáš +2 more
openaire +2 more sources
Commuting Pairs in Quasigroups
Journal of Combinatorial Designs, Volume 33, Issue 11, Page 418-427, November 2025.ABSTRACT A quasigroup is a pair ( Q , ∗ ), where Q is a nonempty set and ∗ is a binary operation on Q such that for every ( a , b ) ∈ Q 2, there exists a unique ( x , y ) ∈ Q 2 such that a ∗ x = b = y ∗ a. Let ( Q , ∗ ) be a quasigroup. A pair ( x , y ) ∈ Q 2 is a commuting pair of ( Q , ∗ ) if x ∗ y = y ∗ x.
Jack Allsop, Ian M. Wanless
wiley +1 more source
On methods of constructing AD-quasigroups
Acta et Commentationes: Ştiinţe Exacte şi ale NaturiiWe research T-quasigroups with AD identity and Schweitzer identity. The necessary and sufficient condition has been determined that in the T-quasigroup G of the form x • y=ϕ(x)+ψ(y), AD identity and the Schweitzer identity are true.
Liubomir Chiriac +2 more
doaj +1 more source
Canonical Labeling of Latin Squares in Average‐Case Polynomial Time
Random Structures &Algorithms, Volume 66, Issue 4, July 2025.ABSTRACT A Latin square of order n$$ n $$ is an n×n$$ n\times n $$ matrix in which each row and column contains each of n$$ n $$ symbols exactly once. For ε>0$$ \varepsilon >0 $$, we show that with high probability a uniformly random Latin square of order n$$ n $$ has no proper subsquare of order larger than n1/2log1/2+εn$$ {n}^{1/2}{\log}^{1/2 ...
Michael J. Gill +2 more
wiley +1 more source
On a method of constructing topological quasigroups obeying certain laws
Acta et Commentationes: Ştiinţe Exacte şi ale NaturiiA new method of constructing non-associative topological quasigroups obeying certain laws is given. Also, in this paper we research T-quasigroups with Abel-Grassmann identity (ab)•c=(cb)•a.
Liubomir Chiriac +2 more
doaj +1 more source
3D compatible ternary systems and Yang-Baxter maps
, 2013 According to Shibukawa, ternary systems defined on quasigroups and satisfying certain conditions provide a way of constructing dynamical Yang-Baxter maps. After noticing that these conditions can be interpreted as 3-dimensional compatibility of equations
Kouloukas, Theodoros E. +1 more
core +1 more source
Mathematica Slovaca, 2011 Abstract Napoleon’s quasigroups are idempotent medial quasigroups satisfying the identity (ab·b)(b·ba) = b. In works by V. Volenec geometric terminology has been introduced in medial quasigroups, enabling proofs of many theorems of plane geometry to be carried out by formal calculations in a quasigroup.
openaire +3 more sources
Extensions of Steiner Triple Systems
Journal of Combinatorial Designs, Volume 33, Issue 3, Page 94-108, March 2025.ABSTRACT In this article, we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a ...
Giovanni Falcone +2 more
wiley +1 more source
Quantum Quasigroups and the Quantum Yang–Baxter Equation
Axioms, 2016 Quantum quasigroups are algebraic structures providing a general self-dual framework for the nonassociative extension of Hopf algebra techniques. They also have one-sided analogues, which are not self-dual.
Jonathan Smith
doaj +1 more source