FALCÓN GANFORNINA , Raúl Manuel

El "fenómeno Sudoku", iniciado en España en el año 2005, ha alcanzado un éxito destacable. Tratándose de un juego en el que la lógica matemática está en todo momento presente, los Sudokus han logrado una adición que pocos pasatiempos han logrado crear anteriormente. Se han realizado publicaciones expresamente dedicadas únicamente a dicho juego...

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 classify such structures according to more general symmetries. Since then, a wide range of applications have arisen in the...

Evolution algebras were introduced into Genetics to deal with the mechanism of inheritance of asexual organisms. Their distribution into isotopism classes is uniquely related with the mutation of alleles in nonMendelian Genetics. This paper deals with such a distribution by means of Computational Algebraic Geometry. We focus in particular on...

Any gene mutation during the mitotic cell cycle of a eukaryotic cell can be algebraically represented by an isotopism of the evolution algebra describing the genetic pattern of the inheritance process. We identify any such pattern with a total-colored graph so that any isotopism of the former is uniquely related to an isomorphism of the latter....

El presente trabajo trata la distribución del conjunto $\mathcal{F}_n^p$ de álgebras de Lie filiformes de dimensión $n$ sobre $\mathbb{Z}/p\mathbb{Z}$ en clases isomórficas e isotópicas. Se estudian para ello distintas propiedades que deben verificar las aplicaciones lineales correspondientes, al mismo tiempo que se identifica dicho conjunto...

In the current paper, we study the distribution into isotopism and isomorphism classes of the relevant family FpnFnp of Lie algebras of basis {e1,…,en}{e1,…,en} and nonzero brackets [ei,en]∈⟨e1,…,en−1⟩[ei,en]∈⟨e1,…,en−1⟩ over a finite field FpFp , with p prime. At this end we first introduce the concept of the structure tuple of a Lie...

In this communication we deal with a class of emerging algebras called evolution algebras. These algebras were firstly introduced by J. P. Tian, and then jointly presented with Vojtechovsky in 2006 [6], and later appeared as a book by Tian in 2008 [5]. The motivation to consider these algebras, which lie between algebras and dynamical systems,...

The mutation graph of an asexual diploid organism is introduced as an edgecolouredgraph derived from the genetic pattern by isotopisms of an evolution algebraover a finite field. We describe the step-by-step construction of this graph and establishsome of its basic properties. In order to illustrate this construction, we focus on thespectrum of...

The set of Mn(K) of n-dimensional Malcev magma algebras over a finite field can be identified with algebraic sets defined by zero-dimensional radical ideals for which the computation of their reduced Gröbner bases makes feasible their enumeration and distribution into isomorphism and isotopism classes. Based on this computation and the...

Lo que se pretende en la presente comunicación es hacer entender que disponer de una mascota en una clase de Matemáticas es no sólo posible sino que, llegado el caso, es incluso aconsejable. Para ello compartiremos la experiencia que tuvimos con el alumnado de Sevilla, comprendido entre 6º de Primaria y 2º de ESO, ambos niveles inclusive, con...

The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic Geometry to determine the distribution of three-dimensional evolution algebras over any field into isotopism...

The distribution of algebras into equivalence classes is usually done according to the concept of isomorphism. However, such a distribution can also be done into isotopism classes. The concept of isotopism was explicitly introduced in 1942 by Abraham Adrian Albert to classify non-associative algebras. In this poster we deal with the study of...

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Since the introduction of the concept of isotopism of algebras by Albert in 1942, a prolific literature on the subject has been developed for distinct types of algebras. Nevertheless, there barely exists any result on the problem of distributing Lie algebras into isotopism classes. The current paper is a first step to deal with such a problem....

This paper addresses the distribution into isomorphism and isotopism classes of the set Mn,p of n-dimensional Malcev algebras over the finite field Fp, with p prime. This distribution is explicitly determined for dimension 2 and for the sets M3,p, with p<=7.

This paper provides an in-depth analysis of how computer algebra systems and CSP solvers can be used to deal with the problem of enumerating and distributing the set of $r\times s$ partial Latin rectangles based on $n$ symbols according to their weight, shape, type or structure. The computation of Hilbert functions and triangular systems of...

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Triples of a Latin square L and isotopisms of its autotopism group U (L) can be used to get a secret sharing scheme in Cryptography. Although the weight of in formation given by the latter is usually greater than that given by the former, the size of an isotopism is generally much larger than that of a triple. As this problem rises with n, it...

La integración en el proceso de enseñanza-aprendizaje de herramientas informáticas que requieren una participación activa del alumnado favorece la comprensión efectiva de conceptos y razonamientos. Cuando se realiza una distinción entre clases teórico-prácticas y prácticas de informática, esta integración suele ser parcial, lo que produce en el...