English

Some Smallest Parts Functions from Variations of Bailey's Lemma

Number Theory 2017-04-06 v4

Abstract

We construct new smallest parts partition functions and smallest parts crank functions by considering variations of Bailey's Lemma and conjugate Bailey pairs. The functions we introduce satisfy simple linear congruences modulo 33 and 55. We introduce and give identities for two four variable qq-hypergeometric functions; these functions specialize to some of our new spt-crank-type functions as well as many known spt-crank-type functions.

Keywords

Cite

@article{arxiv.1506.05344,
  title  = {Some Smallest Parts Functions from Variations of Bailey's Lemma},
  author = {Chris Jennings-Shaffer},
  journal= {arXiv preprint arXiv:1506.05344},
  year   = {2017}
}