Results 31 to 40 of about 1,056 (96)

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, Adam Mammoliti, Ian M. Wanless   +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, Agota Figula, Mario Galici   +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

Cheban loops

, 2010
Left Cheban loops are loops that satisfy the identity x(xy.z) = yx.xz. Right Cheban loops satisfy the mirror identity {(z.yx)x = zx.xy}. Loops that are both left and right Cheban are called Cheban loops.
Phillips, J. D., Shcherbacov, V. A.
core   +1 more source

Exceptional smooth Bol loops

International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 9, Page 575-579, 2002., 2002
One new class of smooth Bol loops, exceptional Bol loops, is introduced and studied. The approach to the Campbell‐Hausdorff formula is outlined. Bol‐Bruck loops and Moufang loops are exceptional which justifies our consideration.
Larissa V. Sbitneva
wiley   +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

Axioms for trimedial quasigroups [PDF]

, 2003
We give new equations that axiomatize the variety of trimedial quasigroups. We also improve a standard characterization by showing that right semimedial, left F-quasigroups are trimedial.Comment: 6 pages, AMS-LaTeX. To appear in Comment. Math.
Kinyon, Michael K., Phillips, J. D.
core   +3 more sources

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., Papageorgiou, Vassilios G.   +1 more
core   +1 more source

A Unified Approach to Image Recognition and Cryptography via Flexible Weak Inverse Property Quasigroups

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, Muhammad Nadeem, Muhammad Kamran, Muhammad Arshad, Samuel Asefa Fufa, Abdul Rauf Khan   +5 more
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, Jaiyeola, Temitope Gbolahan   +1 more
core   +1 more source