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A proof of some conjectures of Mao on partition rank inequalities

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Abstract

Based on work of Atkin and Swinnerton-Dyer on partition rank difference functions, and more recent work of Lovejoy and Osburn, Mao has proved several inequalities between partition ranks modulo 10, and additional results modulo 6 and 10 for the \(M_2\) rank of partitions without repeated odd parts. Mao conjectured some additional inequalities. We prove some of Mao’s rank inequality conjectures for both the rank and the \(M_2\) rank modulo 10 using elementary methods.

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Notes

  1. We note that our definition of \(L_{a,b}\) differs from Mao’s in that the roles of a and b are reversed.

References

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Authors and Affiliations

  1. Emory University, Atlanta, GA, USA

    Ethan Alwaise

  2. Vassar College, Poughkeepsie, NY, USA

    Elena Iannuzzi

  3. Department of Mathematics, Oregon State University, 368 Kidder Hall, Corvallis, OR, 97331, USA

    Holly Swisher

Authors
  1. Ethan Alwaise
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  2. Elena Iannuzzi
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  3. Holly Swisher
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Corresponding author

Correspondence to Holly Swisher.

Additional information

This work was supported by the National Science Foundation REU Grant DMS-1359173.

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Alwaise, E., Iannuzzi, E. & Swisher, H. A proof of some conjectures of Mao on partition rank inequalities. Ramanujan J 43, 633–648 (2017). https://doi.org/10.1007/s11139-016-9789-x

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  • DOI: https://doi.org/10.1007/s11139-016-9789-x

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