Inequalities for positive rank and crank moments of overpartitions Public Deposited

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  • In recent work, Andrews, Chan, and Kim extend a result of Garvan about even rank and crank moments of partitions to positive moments. In a similar fashion we extend a result of Mao about even rank moments of overpartitions. We investigate positive Dyson-rank, M₂-rank, first residual crank, and second residual crank moments of overpartitions. In particular, we prove a conjecture of Mao which states that the positive Dyson-rank moments are larger than the positive M₂-rank moments. We also prove some additional inequalities involving rank and crank moments of overpartitions, including an interlacing property.
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  • Larsen, A., Rust, A., & Swisher, H. (2014). Inequalities for positive rank and crank moments of overpartitions. International Journal of Number Theory, 10(08), 2115-2133. doi:10.1142/S1793042114500717
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