(2026) Together with Jean-Luc Baril and Rigoberto Flórez, we introduce two families of generalized Narayana arrays arising from Dyck paths whose peaks or valleys are restricted according to their heights. The first family records the number of peaks or valleys occurring at heights in a prescribed set, while the second requires all peaks or valleys to lie in that set. We derive bivariate generating functions for several natural choices of heights, including consecutive levels, even and odd heights, and arithmetic progressions, and we obtain asymptotic estimates for the corresponding statistics. The paper also develops bijections with 132-avoiding permutations, integer compositions, Motzkin paths, and pattern-avoiding full binary trees, revealing connections with classical sequences such as the Catalan, Pell, Motzkin, and Riordan numbers. This work appears in our article Generalized Narayana Arrays, Restricted Dyck Paths, and Related Bijections, published in the Australasian Journal of Combinatorics.

(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.

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