FALCÓN GANFORNINA , Óscar Jesús

El presente manuscrito trata distintos aspectos de la teoría de isotopismos de álgebras, centrándose en particular en los isotopismos de álgebras de Lie, de Malcev y de evolución, los cuáles no han sido suficientemente estudiados en la literatura. La distribución que sigue el manuscrito se detalla a continuación. En el Capítulo 1 se expone un...

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...

Conjugacy and orthogonality of Latin squares have been widely studied in the literature not only for their theoretical interest in combinatorics, but also for their applications in distinct fields as experimental design, cryptography or code theory, amongst others. This paper deals with a series of binary constraints that characterize the sets...

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...

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....

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...

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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...

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...

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...

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...

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.

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...

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...

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....

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...

En Criptografía, la eficacia de un generador de secuencias pseudo-aleatorias viene determinada por el periodo de crecimiento en la secuencia generada. En el caso concreto de generadores basados en elementos líderes y cuadrados latinos, existen diversos análisis estadísticos que confirman la importancia que adquiere una óptima elección del...

En este artículo se presenta una visión global de lo que se entiende por WebQuest (WQ en lo sucesivo) y se muestra su posible utilización por el profesor de Matemáticas de Secundaria y de Bachillerato para motivar al alumnado en sus clases y despertar en él el interés y el gusto por la asignatura. Se comentan algunas de las escasas WQ...