Arithmetic properties of colored p-ary partitions

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 α and k = p α - 1 . We also prove a general result concerning the case in which finitely many parts...

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Published in:Acta mathematica Hungarica 2023-11, Vol.171 (1), p.53-66
Main Author: Żmija, B.
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description 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 α and k = p α - 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).
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title Arithmetic properties of colored p-ary partitions
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