(04/2024) During the 20th International Conference on Fibonacci Numbers and Their Applications (2022) , Brian Hopkins talked about Arndt compositions, and proved  several interesting properties using combinatorial arguments. Now, jointly with Daniel Checa, we have obtained several beautiful and new results using generating functions! (see our paper in INTEGERS).

(03/2024) With Rigo, we introduced both symmetric and asymmetric statistic in Dyck paths. Now, in collaboration with Jean-Luc, we have investigated this interesting parameter in Dyck paths with air pocktes.  Our results have been published in the paper titled Symmetries in Dyck paths with air pockets (in Aequationes Mathematice).

(02/2024) We have completed our study on classical and consecutive pattern avoidance in Catalan words:

• • In our paper titled Last symbol distribution in pattern avoiding Catalan words with Jean-Luc Baril and Javier Gonzalez, published in Mathematics for Computer Sciences,  we have enumerated the last symbol statistic on the sets of Catalan words avoiding a pattern of lenght at most three. We end this paper by describing a computational approach using computer algebra. 

  • In our second paper, titled Consecutive pattern-avoidance in Catalan words according to the last symbol co-authored with Jean-Luc Baril, Daniela Colmenanres, Emmanuel Silva, Lina Simbaqueba and Diana Toquica, and published in RAIRO-Theoretical Informatics and Applications, we investigate the distribution of the last symbol statistic on the sets of Catalan words avoiding a consecutive pattern of length at most three.

  • We have also achieved a comprehensive classification of avoiding ordered pair relations and descent distribution in Catalan words. See the paper Descent distribution on Catalan words avoiding ordered pairs of relations, with Jean-Luc Baril, and published in Advances in Applied Mathematics.