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On partitions with initial repetitions

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Abstract

We consider George Andrews’ fundamental theorem on partitions with initial repetitions and obtain some partition identities and parity results. A simplified, diagram-free, version of William Keith’s bijective proof of the theorem is presented. Lastly, we obtain extensions and variations of the theorem using a class of Rogers–Ramanujan-type identities for n-color partitions studied by A.K. Agarwal.

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Acknowledgements

The authors wish to thank an anonymous referee for useful comments which improved the clarity of Sects. 2 and 4.

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, P. O. 2050, Johannesburg, South Africa

    Augustine O. Munagi & Darlison Nyirenda

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  1. Augustine O. Munagi
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  2. Darlison Nyirenda
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Correspondence to Augustine O. Munagi.

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Funding was provided by National Research Foundation (Grant No. 80860).

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Munagi, A.O., Nyirenda, D. On partitions with initial repetitions. Ramanujan J 46, 389–402 (2018). https://doi.org/10.1007/s11139-017-9896-3

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  • DOI: https://doi.org/10.1007/s11139-017-9896-3

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