Exotic Bailey-Slater SPT-Functions III: Bailey Pairs from Groups B, F, G, and J
Abstract
We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by a spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting in the spt-crank-type functions. We find some of the spt-crank-type functions to have interesting representations as single series, some of which reduce to infinite products. Additionally we find dissections of the other spt-crank-type functions when is a certain root of unity. Both methods are used to explain congruences for the spt-type functions. Our series formulas require Bailey's Lemma and conjugate Bailey pairs. Our dissection formulas follow from Bailey's Lemma and dissections of known ranks and cranks.
Keywords
Cite
@article{arxiv.1504.05120,
title = {Exotic Bailey-Slater SPT-Functions III: Bailey Pairs from Groups B, F, G, and J},
author = {Chris Jennings-Shaffer},
journal= {arXiv preprint arXiv:1504.05120},
year = {2015}
}