(2026) Together with Brian Hopkins, we study multicompositions, a generalization of integer compositions in which a bounded number of consecutive zeros are allowed between positive parts. Using formal languages, we derive generating functions that enumerate these objects according to several natural statistics, including the numbers of positive parts, zeros, and occurrences of a given part. We also use Riordan arrays to investigate multicompositions with restricted parts, such as bounded parts, arithmetic progressions, and forbidden values. Through finite automata, we establish connections with pattern-avoiding words, while several special cases lead to generalized Fibonacci and Pell polynomials. Our results also provide new combinatorial interpretations for several sequences and arrays in the OEIS. This work appears in our article Multicompositions via Formal Languages and Riordan Arrays, published in Enumerative Combinatorics and Applications.

(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.

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