[Abstract] George E. Andrews, Frank G. Garvan and Jie Liang; Self-conjugate vector partitions and the parity of the spt-function, preprint.


Abstract: 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.

The url of this page is http://qseries.org/fgarvan/abstracts/spt-parity.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Tuesday, January 10, 2012.
Last update made Tue Jan 10 09:29:12 EST 2012.

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