(05/2004) Jonly with Jean-Luc Baril and Fabio Velandia found a bijection between the set of directed column-convex polyominoes on triangular and honeycomb lattices of area n and some families of restricted compositions. This is an analogous result to one given by Deutsch and Prodinger for polyominoes over square lattices. As a byproduct, we deduce new close forms for the number of hexagonal and triangular directed column-convex polyominoes of area n with k columns. (See our paper in Theoretical Computer Sciences)

(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).

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