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Some Properties of Overpartitions into Nonmultiples of Two Integers
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We consider properties of overpartitions that are simultaneously {\ell}-regular and {\mu}-regular, where {\ell} and {\mu} are positive relatively prime integers. We prove a seven-way combinatorial identity related to these overpartitions. We also prove several congruence properties satisfied by this class of partitions (and a further related class) using both generating functions and modular forms with Radu's Algorithm.
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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New Congruences on Biregular Overpartitions
The paper derives infinite congruence families for several biregular overpartition functions, but the headline family (4,3^t) with t=1 is invalid because \bar{B}_{4,3}(3)=6.
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