Abstract
In 2013, Baruah and Sarmah, and Xia and Yao independently obtained generating function for the sequences p−8(2n + 1) and p−8(4n + 3), where p−8(n) counts the number of partitions of n in eight colours. In this article, we generalize the identities and as a consequence, establish several Ramanujan type congruences modulo higher powers of 2.
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Acknowledgement
We would like to thank the referee and editor for comments. The second named author was partially supported by the University Grants Commission of India, under the Start-Up Research grant no. F.30-489/2019(BSR).
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Dedicated to Prof. Chandrashekar Adiga on the occasion of his 62nd birthday
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Hemanthkumarm, B., Ranganatha, D. & Bharadwaj, H.S.S. On Eight Colour Partitions. Indian J Pure Appl Math 51, 1843–1856 (2020). https://doi.org/10.1007/s13226-020-0500-y
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DOI: https://doi.org/10.1007/s13226-020-0500-y