My research interests can be framed in discrete mathematics and involves enumerative combinatorics, number theory, coding theory and special functions. I like coding and looking out for patterns using computers.
Colored random tilings on grids
(with J. L. Ramirez). Journal of Automata, Languages and Combinatorics, 2025.
Counting Colored Tilings on Grids and Graphs
(with J. L. Ramirez) Proceedings GASCom 2024,2024.
Enumeration of Colored Tilings on Graphs via Generating Functions
(with J. L. Ramirez) RAIRO-ITA.
Symmetric tensor power of graphs
(with W. Astaiza, A. J. Barrios, H. Chimal-Dzul, S. R. Garcia, J. Lopez de la luz, V. H. Moll and Y. Puig). Link Scientia
Preprint
On the cycle structure of the symmetric tensor power of permutations. (with S. Caballero).
The Combinatorics of Motzkin Polyominoes
(with Jean-Luc Baril, Sergey Kirgizov and JL. Ramirez) Discrete Applied Mathematics. Volume 364 , 2025.
Restricted bargraphs and unimodal compositions
(with R. Florez, and J. L. Ramirez) Journal of Combinatorial Theory, Series A, 2024.
Some Connections Between Restricted Dyck Paths, Polyominoes, and Non-Crossing Partition
(with R. Florez, J. L. Ramirez and F. Velandia). Conference proceedings Combinatorics, Graph Theory & Computing, 2024.
Restricted Dyck Paths on Valleys Sequence
(R. Florez, T. Mansour, JL Ramirez and F. Velandia) Séminaire Lotharingien de Combinatoire. 87B, 2023.
Enumeration of r-smooth words over a finite alphabet
(T. Mansour and J. L. Ramirez) Discrete Mathematical Letters, 2023.
A refinement of Dyck paths: a combinatorial approach
(with R. Florez, J. L. Ramirez and F. Velandia). Discrete Mathematics, Algorithms and Applications, 2021.
Inversions in Colored Permutations, Derangements, and Involutions
(with M. Ahmia and J. L. Ramirez). Advances in Applied Math, 2026.
On the r-derangements of type B
(with I. Mezo, V. Moll and J.L. Ramirez). Online Journal of Analytic Combinatorics, 2022.
New modular symmetric function and its applications: Modular s-Stirling numbers
(with M. Ahmia, B. Abdelghafour and J. L. Ramirez). Bulletin of the Malaysian Mathematical Sciences Society, 2022.
A Combinatorial Approach to the Stirling numbers of the First Kind with Higher Level.
(with T. Komatsu and J. L. Ramirez. ) Stud. Sci. Math. Hung, 2021 link.
A Combinatorial Approach to the Generalized Central Factorial Numbers.
(with T. Komatsu and J. L. Ramirez.) Mediterranean Journal of Mathematics, 2021 link. VIDEO
Extensions of set partitions and permutations.
(with J. Caicedo, V. H. Moll and J. L. Ramirez.) Electronic Journal of Combinatorics, 2019. link.
Combinatorial and Arithmetical Properties of the Restricted and Associated Bell and Factorial Numbers.
(with V. H. Moll and J. L. Ramirez ) Journal of Combinatorics, 2018. link.
Eulerian numbers associated with arithmetical progressions.
(with J. L. Ramirez and S. N. Villamarin) Electronic Journal of Combinatorics, 2018. link.
Arithmetic properties of the sum of divisors.
(with T. Amdeberhan, V. H. Moll and V. Sharma.) Journal of Number Theory , 2020 link.
The papers on set partitions also have cool results about p-adic valuations of sequences!
The code here was used as an implementation of the construction of Symmetric power of a graph. Using this code, we conjecture and prove various results that are available in a preprint here.
The code here was used as an implementation of an algorithm for modular decomposition Modular decomposition of graphs and hierarchical modeling by C. Ludena, M. Mendez and N. Bolivar, 2018 . link.