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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. ...
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 ...
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 ...
Artículo
Computation of isotopisms of algebras over finite fields by means of graph invariants
(Elsevier, 2017-07)
In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually ...
Artículo
Partial Latin rectangle graphs and autoparatopism groups of partial Latin rectangles with trivial autotopism groups
(Elsevier, 2017)
An $r \times s$ partial Latin rectangle $(l_{ij})$ is an $r \times s$ matrix containing elements of $\{1,2,\ldots,n\} \cup \{\cdot\}$ such that each row and each column contain at most one copy of any symbol in $\{1,2,\ldots,n\}$. ...