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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.
Forward citations
Cited by 3 Pith papers
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Extending Recent Congruence Results on $(\ell,\mu)$-Regular Overpartitions
New infinite families of congruences for (2,3)-, (4,3)-, and (4,9)-regular overpartitions are proved via classical q-series dissections.
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On Some New Congruences For Biregular Overpartitions
B_{2^alpha,3^beta}(n), the number of overpartitions whose parts avoid multiples of 2^alpha and 3^beta, satisfies new congruence families modulo 4, 8, 6, and 12.
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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.
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