Andrews et al. (Acta Arith. 105:51–66, 2002) introduced and studied the partition function PD(n), the number of partitions of n with designated summands. Recently, congruences involving the number of ℓ-regular partitions with designated summands, denoted by PDℓ(n) , have been explored for specific fixed values of ℓ. In this paper, we provide several families containing infinitely many congruences for PDk(n) for various values of k.
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