(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. 

(2026) The paper studies new families of colored partitions and compositions in which the color of each part is itself a composition or partition of the same size, and it develops several bijections connecting these objects with classical combinatorial structures such as permutations, set partitions, and multiset partitions. These constructions recover familiar sequences, including factorials and Bell numbers, and lead in the second part of the paper to a general framework based on admissible sets of compositions, within which the authors prove a colored analogue of Euler’s partition theorem that extends earlier results of Goyal. This work appears in our article On colored partitions and Euler-type identities published in Integers. 

Old News