(2025) Together with Diego Villamizar, we studied colored tilings of graphs by modeling them as k-colored partitions into connected blocks with distinct adjacent colors. Using bivariate generating functions and combinatorial techniques, we derived enumeration formulas and expected values for families of graphs including trees, cycles, complete and bipartite graphs, as well as Cartesian products such as Km​×Pn​ and star graphs. We obtained explicit functional equations, closed expressions, and asymptotic formulas describing the distribution of block sizes. This work appears in our article Enumeration of Colored Tilings on Graphs via Generating Functions, published in RAIRO – Theoretical Informatics and Applications.

(2025) Together with Jean-Luc Baril, we studied partial Motzkin paths with air pockets (MAP) of the first kind under pattern avoidance constraints. We considered families of paths avoiding peaks, valleys, or double rises, and derived functional equations for their bivariate generating functions with respect to length, final height, and type of last step. Using the kernel method, we obtained closed forms expressed in terms of Riordan arrays and identified connections with known integer sequences. Furthermore, we established constructive bijections between these restricted MAP and families of Dyck or Motzkin paths with modular constraints on peaks and valleys. These results are presented in our article Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises, published in Discrete Mathematics, Algorithms and Applications.

(2025) Together with José L. Herrera and Toufik Mansour, we studied polyominoes arising from inversion sequences, focusing on the distribution of lattice points in their bargraph representation.  We developed recurrence relations and generating functions to enumerate interior vertices, corners, and vertices of given degree, and derived explicit formulas for their total values across all inversion sequences of length n. Using symbolic computer algebra, we obtained closed expressions and functional equations that describe these distributions. This work appears in our article Lattice points on polyominoes of inversion sequences, published in Quaestiones Mathematicae.

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