Pedro Fernando Fernández Espinosa

National University of Colombia | UNAL · Departamento de Matemáticas (Bogotá)

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...

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...

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...

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...

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...

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.

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...

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.

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.

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.

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...

A categorification of the sequence A052558 in the OEIS is given by defining new invariants for indecomposable Kronecker modules.

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...

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...

We prove that the algorithm of differentiation VIII for equipped posets induces a categorical equivalence between quotient categories.

We establish a categorical equivalence induced by the algorithm of differentiation D-IX for equipped posets.

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...