Results 41 to 50 of about 1,056 (96)
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.
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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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Global Left Loop Structures on Spheres [PDF]
, 2000 On the unit sphere $\mathbb{S}$ in a real Hilbert space $\mathbf{H}$, we derive a binary operation $\odot$ such that $(\mathbb{S},\odot)$ is a power-associative Kikkawa left loop with two-sided identity $\mathbf{e}_0$, i.e., it has the left inverse ...
Kinyon, Michael K.
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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
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Conjugate sets of loops and quasigroups. DC-quasigroups
, 2012 It is known that the set of conjugates the conjugate set of a binaryquasigroup can contain 1, 2, 3 or 6 elements. We investigate loops, IP-quasigroupsand T-quasigroups with distinct conjugate sets described earlier. We study in moredetail the quasigroups all conjugates of which are pairwise distinct shortly, DC-quasigroups.
Beleavscaia, G.B., Popovici, T.
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Smarandache Isotopy Theory Of Smarandache: Quasigroups And Loops
, 2007 The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops. The exploration includes: Smarandache; isotopy and isomorphy classes, Smarandache $f,g$ principal isotopes and G-Smarandache loops.
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A Study Of New Concepts In Smarandache Quasigroups And Loops
, 2009 The various areas where loop theory originated and through which it moved during the early part of its 70 years of history can be mapped and fitted not only in a geographical and a chronological sense but also conceptually. Loop theory is of course a relatively young subject which continues to grow day by day.
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