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Acta Arithmetica
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zbMATH Open
Article . 2016
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Acta Arithmetica
Article . 2016 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2015
License: arXiv Non-Exclusive Distribution
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Exotic Bailey–Slater spt-functions III: Bailey pairs from groups B, F, G, and J

Exotic Bailey-Slater spt-functions. III: Bailey pairs from groups B, F, G, and J
Authors: Jennings-Shaffer, Chris;

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 $z=1$ 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 $z$ 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.

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Keywords

Partitions; congruences and congruential restrictions, partition pairs, smallest parts function, Mathematics - Number Theory, Basic hypergeometric functions in one variable, \({}_r\phi_s\), partitions, congruences, FOS: Mathematics, Elementary theory of partitions, Number Theory (math.NT), Andrews' spt function

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
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bronze