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

2016/08/29 by Babecki, Catherine, Jennings-Shaffer, Chris, Sangston, Geoffrey
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1608.08132

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.

Related

• Higher order spt functions for overpartitions, overpartitions with\n smallest part even, and partitions without repeated odd parts
• Some Smallest Parts Functions from Variations of Bailey's Lemma
• Higher Order SPT-Functions
• Asymptotic inequalities for positive crank and rank moments
• Rank and Crank Moments for Partitions without Repeated Odd Parts