(2026) Together with Jean-Luc Baril, we study families of paths that arise naturally in a hexagonal circle packing, a classical geometric arrangement in which each circle touches six neighbors. The paper shows how these paths can be counted according to several natural parameters, such as their width, height, area, number of steps, and kissing number. Beyond the enumeration, we establish connections with well-known combinatorial objects, including Dyck paths, Motzkin paths, Riordan arrays, and continued fractions. The work illustrates how a simple geometric model can lead to rich enumerative structures and unexpected links with classical sequences. This work appears in our paper Enumeration of Paths in a Hexagonal Circle Packing, published in Discrete Mathematics.

(2026 - Apr) Together with Beimar J. Naranjo, we present an expository study of generalized Fibonacci numbers through simple and visual combinatorial models. The paper highlights several bijections between discrete objects such as compositions, graph structures, matchings, Young diagrams, and colored compositions, many of which are counted by Fibonacci numbers or natural variations of them. The aim is to show how these classical sequences arise in different settings and how bijective arguments can reveal the common combinatorial ideas behind them. This work appears in our article Generalized Fibonacci Numbers: Compositions and Graphs, published in Resonance.

(2026) Together with Jean-Luc Baril, we study how classical permutation statistics behave inside two structured families of permutations: increasing permutations and flattened permutations. We obtain explicit exponential generating functions for parameters such as valleys, runs, peaks, and right-to-left minima, and we complement these enumerative results with bijections that clarify the underlying combinatorial structure. The study connects these classes with several familiar enumerative sequences, showing that even within restricted permutation families one finds rich interactions between generating functions, recurrences, and classical combinatorial numbers. This work appears in our article Some distributions on increasing and flattened permutations, published in Aequationes Mathematicae. 

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