arXiv subjects

Pedro Fernando Fernández Espinosa

Publications and source records attributed to Pedro Fernando Fernández Espinosa.

6 recordsLinked to original sources

arXiv2026

On Some Properties of Matrices with Entries Defined by Products of $k$-Fibonacci and $k$-Lucas Numbers

In this paper, we study a structured family of matrices whose entries are given by products of $k$-Fibonacci and $k$-Lucas numbers. For this family, we obtain explicit and unified formulas for several classical matrix invariants, including the determinant, inverse, trace, and matrix powers, revealing nontrivial algebraic patterns induced by the underlying recurrence relations. In addition, we determine the spectral radius and the energy of the graphs naturally associated with these matrices. Finally, we establish connections between the resulting formulas and certain integer sequences recorded in the On-Line Encyclopedia of Integer Sequences (OEIS).

math.CO↗

arXiv2025

On the Number of Exceptional Pairs Over a Class of Nakayama Algebras

In this paper some combinatorial and homological tools are used to describe and give an explicit formula for the number of exceptional pairs (exceptional sequences of length two) for some classes of Nakayama Algebras and for the Auslander algebra of a radical square zero algebra of type $\mathbb{A}_n$. In addition, we explore how the number of exceptional pairs can be connected with some integer sequences in the OEIS (The On-line Encyclopedia of Integer Sequences).

math.CO↗

arXiv2024

Interactions Between Brauer Configuration Algebras and Classical Cryptanalysis to Analyze Bach's Canons

Since their introduction, Brauer configuration algebras (BCAs) and their specialized messages have helped research in several fields of mathematics and sciences. This paper deals with a new perspective on using such algebras as a theoretical framework in classical cryptography and music theory. It is proved that some block cyphers define labeled Brauer configuration algebras. Particularly, the dimension of the BCA associated with a ciphertext-only attack of the Vigenere cryptosystem is given by the corresponding key's length and the captured ciphertext's coincidence index. On the other hand, historically, Bach's canons have been considered solved music puzzles. However, due to how Bach posed such canons, the question remains whether their solutions are only limited to musical issues. This paper gives alternative solutions based on the theory of Brauer configuration algebras to some of the puzzle canons proposed by Bach in his Musical Offering (BWV 1079) and the canon â 4 Voc: Perpetuus (BWV 1073). Specifically to the canon â 6 Voc (BWV 1076), canon 1 â2 (also known as the crab canon), and canon â4 Quaerendo Invenietis. These solutions are obtained by interpreting such canons as ciphertexts (via route and transposition cyphers) of some specialized Brauer messages. In particular, it is noted that the structure or form of the notes used in such canons can be described via the shape of the most used symbols in Bach's works.

math.HO↗

arXiv2021

Homological Ideals as Integer Specializations of Some Brauer Configuration Algebras

In this paper homological ideals associated to some Nakayama algebras are characterized and enumerated via integer specializations of some suitable Brauer configuration algebras. Besides, it is shown how the number of such homological ideals can be connected with the categorification process of Fibonacci numbers defined by Ringel and Fahr.

math.RT↗

arXiv2021

Coxeter's Frieze Patterns Arising from Dyck Paths

Frieze patterns are defined by objects of a category of Dyck paths, to do that, it is introduced the notion of diamond of Dynkin type An. Such diamonds constitute a tool to build integral frieze patterns.

math.RT↗

arXiv2021

Brauer Configuration Algebras and Matrix Problems to Categorify Integer Sequences

Bijections between invariants associated to indecomposable projective modules over some suitable Brauer configuration algebras and invariants associated to solutions of the Kronecker problem and the four subspace problem are used to categorify integer sequences in the sense of Ringel and Fahr. Dimensions of the Brauer configuration algebras and their corresponding centers involved in the different processes are given as well.

math.RT↗