Regular and biregular overpartition counts modulo 2^k are determined by ordinary partitions with fewer than k distinct part sizes, reproducing known modulo-4 results and giving explicit modulo-8 expressions.
Further results on arithmetic properties of biregular overpartitions
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abstract
Recently there has been quite a bit of study carried out related to arithmetic properties of overpartitions into non-multiples of two co-prime integers. The paper [19] by Nadji et al. looked into congruences modulo $3$ and powers of $2$ for certain specific pairs of co-prime integers, while the paper [1] by Alanazi et al. investigated some congruences related to some similar and some different pairs of co-prime integers. In this paper we propose some elegant and elementary proofs of a subset of the congruences given in [1] by using only theta function and dissection identities. We also propose a generic method for proving congruences modulo $8$ which doesn't necessarily use any specific $2$-dissection.
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2026 1verdicts
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Some Comments on Regular Overpartitions modulo $2^k$
Regular and biregular overpartition counts modulo 2^k are determined by ordinary partitions with fewer than k distinct part sizes, reproducing known modulo-4 results and giving explicit modulo-8 expressions.