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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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Correspondence to Holly Swisher.

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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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