Results 31 to 40 of about 1,060 (95)
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
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
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
Nonassociative algebras: a framework for differential geometry
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 60, Page 3777-3795, 2003., 2003 A nonassociative algebra endowed with a Lie bracket, called a torsion algebra, is viewed as an algebraic analog of a manifold with an affine connection. Its elements are interpreted as vector fields and its multiplication is interpreted as a connection. This provides a framework for differential geometry on a formal manifold with a formal connection. A
Lucian M. Ionescu
wiley +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
Non-associative geometry and discrete structure of spacetime [PDF]
, 2000 A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.Comment: LATeX2e file, 11 pages, talk given at "Loop's 99 meeting" (Prague, July 27 - August 1, 1999). To
Nesterov, Alexander I., Sabinin, Lev. V.
core +1 more source
Leveraging Nonassociative Algebra for Spectral Analysis of Anomalies in IoT
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.The constantly changing characteristics of distributed networks and Internet of Things and additionally their susceptibility to anomalies render maintaining security and resilience complicated. This research provides a spectral‐based anomaly detection framework connected with nonassociative algebra, inverse property quasigroup.
Faizah D. Alanazi, Chong Lin
wiley +1 more source
On A Cryptographic Identity In Osborn Loops [PDF]
, 2008 This study digs out some new algebraic properties of an Osborn loop that will help in the future to unveil the mystery behind the middle inner mappings $T_{(x)}$ of an Osborn loop.
Adeniran, John Olusola +1 more
core +1 more source
Journal of Function Spaces, Volume 2025, Issue 1, 2025.Nonassociative algebra presents multiple options for comprehending and dealing with difficulties in graph theory, artificial intelligence, and cryptography. Its distinctive traits introduce genuine concepts and procedures not found in conventional associative algebra, yielding to new results from studies and breakthroughs in multiple disciplines ...
Mohammad Mazyad Hazzazi +5 more
wiley +1 more source
Computing with small quasigroups and loops
, 2007 This is a companion to our lectures GAP and loops, to be delivered at the Workshops Loops 2007, Prague, Czech Republic. In the lectures we introduce the GAP package LOOPS, describe its capabilities, and explain in detail how to use it. In this paper we first outline the philosophy behind the package and its main features, and then we focus on three ...
Nagy, G.P., Vojtĕchovský, P.
openaire +3 more sources