Publication at Faculty of Mathematics and Physics |
2023
Abstract
We study divisibility properties of p-ary partitions colored with k(p - 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of k = p(alpha) and k = p(alpha) - 1.
We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p - 1) and all others with exactly k(p - 1) colors, where k is arbitrary (but fixed).