Abstract
Let PD(n) and PDO(n) count, respectively, the number of partitions of n with designated summands and the number of partitions of n with designated summands where all parts are odd, and let \(PD_t(n)\) and \(PDO_t(n)\) count, respectively, the number of tags (that is, designated summands) in the partitions enumerated by PD(n) and PDO(n). We give elementary proofs of congruences for these partition functions.
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Chern, S., Hirschhorn, M.D. Some results concerning partitions with designated summands. Ramanujan J 54, 385–395 (2021). https://doi.org/10.1007/s11139-019-00198-1
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DOI: https://doi.org/10.1007/s11139-019-00198-1