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On the cycle structure of the symmetric tensor power of permutations
Sebastian Caballero, Diego Villamizar
Problem 8.1 in Astaiza et. al. asks about the relationship between the cycle decomposition of a permutation and that of its symmetric tensor power . In this paper,…
Inversions in Colored Permutations, Derangements, and Involutions
Moussa Ahmia, José L. Ramírez, Diego Villamizar
Arslan, Altoum, and Zaarour introduced an inversion statistic for generalized symmetric groups. In this work, we study the distribution of this statistic over colored permutations,…
Enumeration of Colored Tilings on Graphs via Generating Functions
José L. Ramírez, Diego Villamizar
In this paper, we study the problem of partitioning a graph into connected and colored components called blocks. Using bivariate generating functions and combinatorial techniques,…
The Combinatorics of Motzkin Polyominoes
Jean-Luc Baril, Sergey Kirgizov, José L. Ramírez +1
A word over the set of positive integers is a Motzkin word whenever , , and for . It c…