Pedro Fernando Fernández Espinosa

Pedro Fernando Fernández Espinosa
National University of Colombia | UNAL · Departamento de Matemáticas (Bogotá)

About

17
Publications
1,223
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
27
Citations
Citations since 2017
11 Research Items
21 Citations
2017201820192020202120222023024681012
2017201820192020202120222023024681012
2017201820192020202120222023024681012
2017201820192020202120222023024681012
Introduction
Pedro Fernando Fernández Espinosa currently works at the Department of Mathematics, National University of Colombia. Pedro does research in Theory of Representation of Algebras and Its Applications in combinatorics and number theory. Their current project is 'Categorification of Some Integer Sequences and Its Applications '.

Publications

Publications (17)
Article
UDC 512.5 The homological ideals associated with some Nakayama algebras are characterized and enumerated via integer specializations of some suitable Brauer configuration algebras. In addition, it is shown how the number of these homological ideals can be connected with the process of categorification of Fibonacci numbers defined by Ringel and Fahr...
Article
Full-text available
Recently, Çanakçi and Schroll proved that associated with a string module $ M(w) $ there is an appropriated snake graph $ \mathscr{G} $. They established a bijection between the corresponding perfect matching lattice $ \mathscr{L}(\mathscr{G}) $ of $ \mathscr{G} $ and the canonical submodule lattice $ \mathscr{L}(M(w)) $ of $ M(w) $. We introduce B...
Article
Full-text available
The four subspace problem is a known matrix problem, which is equivalent to determining all the indecomposable representations of a poset consisting of four incomparable points. In this paper, we use solutions of this problem and invariants associated with indecomposable projective modules with some suitable Brauer configuration algebras to categor...
Article
Full-text available
Recently, Postnikov introduced Bert Kostant’s game to build the maximal positive root associated with the quadratic form of a simple graph. This result, and some other games based on Cartan matrices, give a new version of Gabriel’s theorem regarding algebras classification. In this paper, as a variation of Bert Kostant’s game, we introduce a wargam...
Article
Full-text available
Bijections between invariants associated with indecomposable projective modules over some suitable Brauer configuration algebras and invariants associated with solutions of the Kronecker problem are used to categorify integer sequences in the sense of Ringel and Fahr. Dimensions of the Brauer configuration algebras and their corresponding centers i...
Article
Full-text available
In this paper, suitable Brauer configuration algebras are used to give an explicit formula for the number of perfect matchings of a snake graph. Some relationships between Brauer configuration algebras with path problems as the Lindstr\"om problem are described as well.
Article
Full-text available
The energy E(G) of a graph G is the sum of the absolute values of its adjacency matrix. In contrast, the trace norm of a digraph Q, which is the sum of the singular values of the corresponding adjacency matrix, is the oriented version of the energy of a graph. It is worth pointing out that one of the main problems in this theory consists of determi...
Article
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 \({\mathbb {A}}_{n}\). Such diamonds constitute a tool to build integral frieze patterns.
Preprint
Full-text available
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.
Preprint
Full-text available
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.
Preprint
Full-text available
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 the...
Article
Full-text available
A categorification of the sequence A052558 in the OEIS is given by defining new invariants for indecomposable Kronecker modules.
Article
Full-text available
We use techniques of the theory of algorithms of differentiation of posets and P-partitions to describe identities of some one-dimensional compositions involving polygonal and cubic numbers. We also describe with these techniques numbers which can be written as a sum of three square of numbers of a given shape or sequences of numbers which can be w...
Article
Full-text available
Via linear extensions of posets, P-partitions, and some higher dimensional compositions defined previously by the first author et al., we obtain solutions to a generalization of a problem on partitions proposed by G. E. Andrews in 1987. Furthermore, it is given a bijective correspondence between higher dimensional compositions whose parts are polyg...
Article
Full-text available
We prove that the algorithm of differentiation VIII for equipped posets induces a categorical equivalence between quotient categories.
Article
Full-text available
We establish a categorical equivalence induced by the algorithm of differentiation D-IX for equipped posets.
Article
Full-text available
Recently, Vanegas and the first author introduced an algorithm to generate a large amount of emerging images. Such an algorithm uses linear representations of posets and admissible transformations of matrix representations to obtain different kind of gestalts. In this paper, we present an algorithm to extract gestalts of different types from these...

Network

Cited By

Projects

Project (1)
Project
To give categorifications of some integer sequences (in the sense of Ringel and Fahr).