Sum of parts in overpartitions and partitions without repeated odd parts

Frank Garvan; Rishabh Sarma

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arXiv · 2606.14680

Sum of parts in overpartitions and partitions without repeated odd parts

Frank Garvan·Rishabh Sarma

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Abstract

In this paper, we obtain several Ramanujan-type congruences modulo 5 and 7 for sum of certain non-overlined parts in overpartitions classified by parity and sum of certain parts in partitions without repeated odd parts classified by parity. Our proofs for the congruences are elementary, depending only on classical theta function identities.

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Frank Garvan, Rishabh Sarma. 2026-06-12. Sum of parts in overpartitions and partitions without repeated odd parts. https://arxiv.org/abs/2606.14680

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