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On Eight Colour Partitions

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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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Authors and Affiliations

  1. Department of Mathematics, M. S. Ramaiah University of Applied Sciences, Peenya Campus, Bengaluru, Karnataka, 560 058, India

    B. Hemanthkumarm & H. S. Sumanth Bharadwaj

  2. Department of Mathematics, School of Physical Sciences, Central University of Karnataka, Kalaburagi, Karnataka, 570 006, India

    D. Ranganatha

Authors
  1. B. Hemanthkumarm
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  2. D. Ranganatha
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  3. H. S. Sumanth Bharadwaj
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Correspondence to B. Hemanthkumarm, D. Ranganatha or H. S. Sumanth Bharadwaj.

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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

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