Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author, Dyson and Hickerson. As a result we obtain an elementary q-series proof of Ono and Folsom's results for the parity of spt(n). A number of related generating function identities are also obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-1,
author = {George E. Andrews and Frank G. Garvan and Jie Liang},
title = {Self-conjugate vector partitions and the parity of the spt-function},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {199-218},
zbl = {1268.05019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-1}
}
George E. Andrews; Frank G. Garvan; Jie Liang. Self-conjugate vector partitions and the parity of the spt-function. Acta Arithmetica, Tome 161 (2013) pp. 199-218. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-3-1/