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 and . We introduce and give identities for two four variable -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}
}