Congruences for (2, 3)-regular partition with designated summands


Abstract


Let PD_{2, 3}(n) count the number of partitions of n with designated summands in which parts are not multiples of 2 or 3. In this work, we establish congruences modulo powers of 2 and 3 for PD_{2, 3}(n). For example, for each \quad n\ge0 and \alpha\geq0 \quad PD_{2, 3}(6\cdot4^{\alpha+2}n+5\cdot4^{\alpha+2})\equiv 0 \pmod{2^4} and PD_{2, 3}(4\cdot3^{\alpha+3}n+10\cdot3^{\alpha+2})\equiv 0 \pmod{3}.

DOI Code: 10.1285/i15900932v36n2p99

Keywords: Designated summands; Congruences; Theta functions; Dissections

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