Research

Research Projects

• Compositions and partitions of figurate numbers, Funded by District University Francisco José de Caldas, Duration: Six months, 2013.

• Diophantine Equations Whose Solution are Families of Figurate Numbers, Funded by District University Francisco José de Caldas, Duration: 2 years, 2015.

• Categorification of Some Integer Sequences and its applications, Funded by Becas Doctorales Colciencias, Duración: 2 years, 2018.

RESEARCH PAPERS

In preparation

A Partition Formula for The Number of Exceptional Pairs in The Auslander- Reiten Quiver of An,

con I.D.M Gaviria y O.D.B. Miranda.

Published and Accepted

1. Brauer Configuration Algebras Defined by Snake Graphs and Kronecker Modules, Electronic Research Archive, 30, 3087-3110, 2022.

2. Categorification of Integer Sequences Via Brauer Configuration Algebras and the Four Subspace Problem, Mathematics, 2022.

3. Brauer Configuration Algebras and Kronecker Modules to Categorify Integer Sequences, Electronic Research Archive, 2022.

4. Wargaming with Quadratic Forms and Brauer Configuration Algebras, Mathematics, 2022.

5. {0, 1} -Brauer Configuration Algebras and Their Applications in Graph Energy Theory, con Agustín Moreno Cañadas, Isaías Marín Gaviria, Natalia Agudelo Muñetón, Mathematics, 9, 3042, 2021. https://doi.org/10.3390/math9233042.

6. Coxeter’s Frieze Patterns Arising from Dyck Paths, Ricerche di Matematica, con Agustín Moreno Cañadas, Gabriel Bravo Rios, Isaías Marín Gaviria, 2021, https://doi.org/10.1007/s11587-021-00594-0.

7. On Some Relationships Between Snake Graphs and Brauer Configuration algebras, Algebra and Discrete mathematics, con Javier Fernando González, Juan Pablo Herrán, Agustín Moreno Cañadas, José Luis Ramírez, 33, 29-59, 2022.

8. Homological Ideals as Integer Specializations of Some Brauer Configuration Algebras, Ukrainian Mathematical Journal, with Agustín Moreno Cañadas, Aceptado, 2020.

9. Categorification of some integer sequences via Kronecker modules, JP Journal of Algebra, Number Theory and Applications, con Agustín Moreno Cañadas, Isaías Marín, 2016.

10. On Sums of Figurate Numbers by Using Algorithms of Differentiation of Posets, JP Journal of Algebra, Number Theory and Applications, con Agustín Moreno Cañadas, Verónica Cifuentes, 2014.

11. Categorification of Some Integer Sequences, Far East Journal Of Mathematical Sciences (FJMS), con Agustín Moreno Cañadas, Hernan Giraldo, 2014.

12. Representations of a Tetrad to Generate Schemes of Emerging Images, Far East Journal of Mathematical Sciences (FJMS), con Agustín Moreno Cañadas, Isaías Marín, 2013.

13. On the algorithm of differentiation D-IX for equipped posets, JP Journal of Algebra, Number Theory and Applications, con Agustín Moreno Cañadas, Isaías Marín, 2013.

14. On the algorithm of differentiation D-VIII for equipped posets, JP Journal of Algebra, Number Theory and Applications, con Agustín Moreno Cañadas, Isaías Marín, 2013.

15. On a problem of G.E Andrews concerning partitions, JP Journal of Algebra, Number Theory and Applications, con Agustín Moreno Cañadas, Verónica Cifuentes, 2013.

Peer Review

2015 Solution of elementary problem B-1142, The Fibonacci Quarterly.

2015 Solution of elementary problem B-1146, The Fibonacci Quarterly.

Refereeing and reviewing

Reviewer for Zentralblatt.

Reviewer for MathReviews.