Results 51 to 60 of about 2,017 (174)
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
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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
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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
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.
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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
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Linking Bipartiteness and Inversion in Algebra via Graph‐Theoretic Methods and Simulink
Complexity, Volume 2025, Issue 1, 2025.Research for decades has concentrated on graphs of algebraic structures, which integrate algebra and combinatorics in an innovative way. The goal of this study is to characterize specific aspects of bipartite and inverse graphs that are associated with specific algebraic structures, such as weak inverse property quasigroups and their isotopes ...
Mohammad Mazyad Hazzazi +6 more
wiley +1 more source
Quasigroups in cryptology [PDF]
Computer Science Journal of Moldova, 2009 We give a review of some known published applications of quasigroups in cryptology.
V.A. Shcherbacov
doaj
On groupoids with Bol-Moufang type identities [PDF]
Computer Science Journal of Moldova, 2020 We present results about groupoids of small order with Bol-Moufang type identities both classical and non-classical which are listed in [7], [9].
Grigorii Horosh +3 more
doaj
Characters of Finite Quasigroups
European Journal of Combinatorics, 1984 In this paper the authors study some of the basics of a character theory for finite non-empty quasigroups, generalizing the traditional ordinary character theory for groups. The authors present the relevant notions from quasigroup theory (the multiplication group, quasigroup conjugacy classes, and the space of class functions) which enable one to apply
Kenneth W. Johnson, Jonathan D. H. Smith
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International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.Research on the confluence of algebra, graph theory, and machine learning has resulted in significant discoveries in mathematics, computer science, and artificial intelligence. Polynomial coefficients can be beneficial in machine learning. They indicate feature significance, nonlinear interactions, and error dynamics.
Faizah D. Alanazi, Theodore Simos
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