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.
Some Properties of Overpartitions into Nonmultiples of Two Integers
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abstract
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.
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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.