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Inequalities for positive rank and crank moments of overpartitions Öffentlichkeit Deposited

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https://ir.library.oregonstate.edu/concern/articles/jh343v225

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Abstract
  • 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.
  • This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by the World Scientific Publishing Company and can be found at: http://www.worldscientific.com/worldscinet/ijnt
  • Keywords: Moments, Crank, Overpartitions, Partitions, Rank
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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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  • 10
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  • 8
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  • This work was supported by the National Science Foundation REU Grant DMS-0852030.
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