My research interests can be framed in  discrete mathematics and involves enumerative combinatorics, number theory, coding theory and special functions. 

Preprints and to appear:

1. 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

2. Colored random tilings on grids (with J. L. Ramirez). to appear in Journal of Automata, Languages and Combinatorics.

3.  Restricted Dyck Paths on Valleys Sequence.(with  . Flórez, T. Mansour, J. L Ramírez, F. A Velandia) to appear in Séminaire Lotharingien de Combinatoire link.    VIDEO

4. Some Connections  Between Restricted Dyck Paths, Polyominoes, and Non-Crossing Partition (with R. Florez, J. L. Ramirez and F. Velandia). to appear in Conference proceedings Combinatorics, Graph Theory & Computing. Link

Journal Articles:

1. Enumeration of r-smooth words over a finite alphabet (T. Mansour and J. L. Ramirez) Discrete Mathematical Letters, 2023. 

2. On the r-derangements of type B (with I. Mezo, V. Moll and J.L. Ramirez). Online Journal of Analytic Combinatorics, 2022.

3. 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.

4. A refinement of Dyck paths:  a combinatorial approach (with R. Florez, J. L. Ramirez and F. Velandia). Discrete Mathematics, Algorithms and Applications, 2021.

5. 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. 

6.  A Combinatorial Approach to the Generalized Central Factorial Numbers.  (with T. Komatsu and J. L. Ramirez.) Mediterranean Journal of Mathematics, 2021 link.    VIDEO

7. Arithmetic properties of the sum of divisors.  (with T. Amdeberhan, V. H. Moll and  V. Sharma.) Journal of Number Theory , 2020 link.

8.  Extensions of set partitions and permutations. (with J. Caicedo, V. H. Moll and J. L. Ramirez.) Electronic Journal of Combinatorics,  2019. link.

9.  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.

10.  Eulerian numbers associated with arithmetical progressions. (with J. L. Ramirez and S. N. Villamarin) Electronic Journal of Combinatorics, 2018. link.

Coding Projects:

1. 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.

2. 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.