Abstract
For any positive integers n and r, let \(p_r(n)\) denotes the number of partitions of n where each part has r distinct colours. Many authors studied the partition function \(p_r(n)\) for particular values of r. In this paper, we prove some general congruences modulo 5 and 7 for the colour partition function \(p_r(n)\) by considering some general values of r. To prove the congruences we employ some q-series identities which are also in the spirit of Ramanujan.
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Communicated by Samy Ponnusamy.
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Saikia, N., Boruah, C. General congruences modulo 5 and 7 for colour partitions. J Anal 29, 917–926 (2021). https://doi.org/10.1007/s41478-020-00287-1
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DOI: https://doi.org/10.1007/s41478-020-00287-1