Combinatorial Identities Corner...

Combinatorial Properties of Integer Compositions

Palindromic and colored superdiagonal compositions

with J. L. Mantilla* and W. Olaya-León. Revista Colombiana de Matemáticas 56(2) (2022), 133-143. (pdf, web)

n-Color palindromic compositions with restricted subscripts

with J. Bravo, J. L. Herrera, and M. Shattuck. Proceedings Mathematical Sciencies (Springer). 131(9) (2021), 1–13. (web)

Combinatorial Properties of Lattice Paths

Enumerating symmetric pyramids in Motzkin paths

with R. Flórez.Ars Mathematica Contemporanea, 23(4)(2023), #P4.06. (web, pdf).

Enumeration of Fuss-skew paths

with T. Mansour.Annales Mathematicae et Informaticae, 55 (2022), 125-136. (pdf, web)

On some relationships between snake graphs and Brauer configuration algebras

with P. Espinosa, J. González*, J. Herrán*, and A. Moreno. Algebra and Discrete Mathematics. 33 (2022), 29–59. (web, pdf)

Counting prefixes of skew Dyck path

with J.L. Baril and L. Simbaqueba*.Journal of Integer Sequences, 24 (2021), Article 21.9.2. (pdf, web)

Counting asymmetric weighted pyramids in non-decreasing Dyck paths

with R. Flórez and L. Junes.The Australasian Journal of Combinatorics. 79(1) (2021), 123–140. (pdf, web)

Some enumerations on non-decreasing Motzkin paths,

with R. Flórez.The Australasian Journal of Combinatorics. 72(1) (2018), 138–154. (web, pdf)

The Pascal rhombus and the generalized grand Motzkin paths,

The Fibonacci Quarterly, 54(2) (2016), 99–104. (web, pdf, arXiv)

I enjoy studying and proving combinatorial identities. I also find interesting the arithmetical and combinatorial properties of sequences like Fibonacci numbers, Pell numbers, Bernoulli polynomials, etc.

Some of the topics (not all) covered in some of these papers are well-suited for undergraduate students. These results can be accessible and engaging for undergraduate students. So, these topics provide an opportunity for students to explore various techniques and approaches in combinatorics and computer algebra systems.

The dual of number sequences, Riordan polynomials, and Sheffer polynomials.

with T.-X. He,Special Matrices, 10(2022), 153-165. pdf

Combinatorial interpretation of generalized Pell numbers.

with J. J. Bravo and J. L. Herrera.Journal of Integer Sequences, 23 (2020), Article 20.2.1. pdf

Convolutions of the bi-periodic Fibonacci numbers.

with T. Komatsu.Hacettepe Journal of Mathematics and Statistics, 49 (2) (2020), 565-577.

Generalized Jacobsthal numbers and restricted k-ary words.

with M. Shattuck. Pure Mathematics and Applications, 28(1)(2019), 91--108. pdf

A multi-parameter generalization of the symmetric algorithm.

with M. Shattuck. Mathematica Slovaca, 68(4)(2018), 699--712. web

A q-symmetric algorithm and its applications to some combinatorial sequences.

with I. Mező.Online Journal of Analytic Combinatorics, 12(7)(2017) #7, 1--13. pdf

Some results on q-analogue of the Bernoulli, Euler and Fibonacci Matrices.

with G. Infante* and A. Sahin. Mathematical Reports (Romanian Academy), 19(4)(2017).

Determinantal and permanental representations of convolved Lucas polynomials.

with V. A. Sahin. Applied Mathematics and Computation, 281, 314--322, 2016. web

A q-analogue of the biperiodic Fibonacci sequence.

with V. Sirvent. Journal of Integer Sequences, 19, article 16.4.6, 2016. pdf

An identity of Carlitz and its generalizations.

American Mathematical Monthly, 123(3), 295, 2016. web

Hessenberg matrices and the generalized Fibonacci-Narayana sequence.

Filomat, {29}(7), 1557--1563, 2015.

A note on the k-Narayana sequence.

with V. Sirvent. Annales Mathematicae et Informaticae, 42, 83-92, 2015

Incomplete generalized Fibonacci and Lucas polynomials.

Hacettepe Journal of Mathematics and Statistics, 44 (2), 363-373, 2015.

On convolved generalized Fibonacci and Lucas polynomials.

Applied Mathematics and Computation, 229(25), 208--213, 2014. web

Incomplete tribonacci numbers and polynomials.

with V. Sirvent. Journal of Integer Sequences, 17, article 14.4.2, 2014

Bi-periodic incomplete Fibonacci sequences.

Annales Mathematicae et Informaticae, 42, 83-92, 2013.

Conference Proceedings

Matrices in the Determinant Hosoya Triangle

with M. Blair*, R. Flórez, and A Mukherjee.The Fibonacci Quarterly (Proceedings of the 19th International Conference on Fibonacci Numbers and Their Applications) 58(5) (2020), 34-54 (web, pdf)

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