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arXiv · 1608.08132

Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs

Catherine Babecki·Chris Jennings-Shaffer·Geoffrey Sangston
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Abstract

We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduce a rank-like function, establish inequalities with the moments of the rank-like function and an associated crank-like function, and give an associated so called higher order smallest parts function. In some cases we are able to deduce inequalities among the rank-like functions. We also conjecture additional inequalities and a large number of congruences for the higher order smallest parts functions.

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Catherine Babecki, Chris Jennings-Shaffer, Geoffrey Sangston. 2016-08-29. Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs. https://arxiv.org/abs/1608.08132

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