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arXiv · 1509.06039

A proof of some conjectures of Mao on partition rank inequalities

Ethan Alwaise·Elena Iannuzzi·Holly Swisher
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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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Ethan Alwaise, Elena Iannuzzi, Holly Swisher. 2015-09-20. A proof of some conjectures of Mao on partition rank inequalities. https://arxiv.org/abs/1509.06039

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