Results 41 to 50 of about 160,139 (111)
SAC loops and loops of order five
Математика, інформатика, фізика: наука та освітаIn this article, we continue the analytical research of small-order loops. Namely, we investigate loops of order 5. Recall that an element of a loop is called unipotent if its square is neutral.
Fedir Sokhatsky
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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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Computing with small quasigroups and loops
, 2015 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, Gábor P., Vojtěchovský, Petr
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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
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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
Row‐Hamiltonian Latin squares and Falconer varieties
Proceedings of the London Mathematical Society, Volume 128, Issue 1, January 2024.Abstract A Latin square is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square L$L$ is row‐Hamiltonian if the permutation induced by each pair of distinct rows of L$L$ is a full cycle permutation. Row‐Hamiltonian Latin squares are equivalent to perfect 1‐factorisations of complete bipartite graphs.
Jack Allsop, Ian M. Wanless
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Graphs Connected to Isotopes of Inverse Property Quasigroups: A Few Applications
Journal of Applied Mathematics, Volume 2024, Issue 1, 2024.Many real‐world applications can be modelled as graphs or networks, including social networks and biological networks. The theory of algebraic combinatorics provides tools to analyze the functioning of these networks, and it also contributes to the understanding of complex systems and their dynamics.
Muhammad Nadeem +3 more
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Lattice-ordered loops and quasigroups
Journal of Algebra, 1970 AbstractIn studying the effect of an order on non-associative systems such as loops or quasigroups, a natural question to ask is whether some order condition which implies commutativity in the group case implies associativity in the corresponding loop case.
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Eigenvalues of Relatively Prime Graphs Connected with Finite Quasigroups
Journal of Mathematics, Volume 2024, Issue 1, 2024.A relatively new and rapidly expanding area of mathematics research is the study of graphs’ spectral properties. Spectral graph theory plays a very important role in understanding certifiable applications such as cryptography, combinatorial design, and coding theory.
Muhammad Nadeem +6 more
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Complexity, Volume 2024, Issue 1, 2024.Taking into account the most recent improvements in graph theory and algebra, we can associate graphs of some mathematical structures with certifiable, widely known applications. This paper seeks to explore the connections established through edge labeling among Latin squares derived from Moufang quasigroups, which are constructed using additive ...
Mohammad Mazyad Hazzazi +5 more
wiley +1 more source