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Mostrando ítems 1-10 de 13
Artículo
Set-independence graphs of vector spaces and partial quasigroups
(Yildiz Technical University, 2023-09-04)
As a generalization of independence graphs of vector spaces and groups, we introduce the notions of set-independence graphs of vector spaces and partial quasigroups. The former are characterized for finite-dimensional ...
Artículo
A new quasigroup isomorphism invariant arising from fractal image patterns
(Chişinău: Institutul de Matematică şi Informatică "Vladimir Andrunachievici", 2022)
The analysis and recognition of fractal image patterns derived from Cayley tables has turned out to play a relevant role for distributing distinct types of algebraic and combinatorial structures into isomorphism classes. ...
Ponencia
Santilli's autotopism of associative partial quasigroups
(International Academic Press, 2007)
In this paper, given an isotopism Θ ∈ In, we study some properties of the set SAPLS(Θ) of those partial Latin squares being the multiplication table of an associative partial quasigroup having Θ as a Santilli’s autotopism.
Artículo
A historical perspective of the theory of isotopisms
(MDPI, 2018-08-03)
In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and ...
Ponencia
Latin squares associated to principal autotopisms of long cycles. Application in Cryptography
(2006-04)
Fixed a principal isotopism $\Theta=(\alpha,\beta,\epsilon)\in S_n^3$, where $S_n$ is the symmetric group of the set $N=\{0,1,...,n-1\}$, we are going to study in this paper the number $\Delta(\Theta)$ of Latin squares ...
Artículo
Computing autotopism groups of partial Latin rectangles: A pilot study
(Wiley, 2019)
Computing the autotopism group of a partial Latin rectangle can be performed in a variety of ways. This pilot study has two aims: (a) to compare these methods experimentally, and (b) to identify the design goals one ...
Artículo
A computational approach to analyze the Hadamard quasigroup product
(American Institute of Mathematical Sciences (AIMS), 2023-03-30)
Based on the binary product described by any Latin square, the Hadamard quasigroup product is introduced in this paper as a natural generalization of the classical Hadamard product of matrices. The successive iteration of ...
Artículo
Cycle structures of autotopisms of the Latin squares of order up to 11
(2012)
The cycle structure of a Latin square autotopism Θ = (α, β, γ) is the triple (lα, lβ, lγ), where lδ is the cycle structure of δ, for all δ ∈ {α, β, γ}. In this paper we study some properties of these cycle structures and, ...
Artículo
Gröbner bases and the number of Latin squares related to autotopisms of order ≤7
(Elsevier, 2007)
Latin squares can be seen as multiplication tables of quasigroups, which are, in general, noncommutativeand non-associative algebraic structures. The number of Latin squares having a fixed isotopismin their autotopism group ...
Artículo
A census of critical sets based on non-trivial autotopisms of Latin squares of order up to five
(AIMS Press, 2020)
This paper delves into the study of critical sets of Latin squares having a given isotopism in their autotopism group. Particularly, we prove that the sizes of these critical sets only depend on both the main class of ...