(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. 

(2025) Together with Moussa Ahmia and Diego Villamizar, we studied inversion statistics on colored permutations, including the subclasses of colored derangements and colored involutions. Using a bijective correspondence between colored permutations and colored Lehmer codes, we developed a unified framework that yields explicit formulas, recurrence relations, and generating functions for colored Mahonian numbers, extending classical results to arbitrary colorings. We further obtained closed expressions for the total number of inversions in colored derangements via inclusion–exclusion, and we established enumeration formulas and exponential generating functions for colored involutions. These results appear in our paper Inversions in colored permutations, derangements, and involutions, published in Advances in Applied Mathematics.

(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.

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