Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J

Chris Jennings-Shaffer. "Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J." Acta Arithmetica 173.4 (2016): 317-364. <http://eudml.org/doc/286173>.

@article{ChrisJennings2016,
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 an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. 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 z 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.},
author = {Chris Jennings-Shaffer},
journal = {Acta Arithmetica},
keywords = {Andrews' spt-function; partitions; partition pairs; smallest parts function; congruences; bailey pairs; bailey's lemma; conjugate bailey pairs},
language = {eng},
number = {4},
pages = {317-364},
title = {Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J},
url = {http://eudml.org/doc/286173},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Chris Jennings-Shaffer
TI - Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 4
SP - 317
EP - 364
AB - 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 an spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting z = 1 in this definition. 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 z 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.
LA - eng
KW - Andrews' spt-function; partitions; partition pairs; smallest parts function; congruences; bailey pairs; bailey's lemma; conjugate bailey pairs
UR - http://eudml.org/doc/286173
ER -