
arXiv: 1504.05120
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.
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
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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