Congruences for Hyper m-ary Overpartition Functions

Abstract We discuss a new restricted m-ary overpartition function , which is the number of hyper m-ary overpartitions of n, such that each power of m is allowed to be used at most m times as a non-overlined part. In this note we use generating function dissections to prove the following family of congruences for all n ≥ 0, m ≥ 4, j ≥ 0, 3 ≤ k ≤ m – 1, and t ≥ 1:

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