Abstract:

Bringmann, Lovejoy, and Osburn showed that the generating functions of the spt-overpartition functions spt(n), spt1(n), spt2(n), and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences mod 5 and 7 for spt (n). Chen, Ji, and Zang were able to define this spt-crank in terms of ordinary partitions. In this paper we define spt-cranks in terms of vector partitions that combinatorially explain the known simple congruences for all the spt-overpartition functions as well as new simple congruences. For all the overpartition functions except M2spt(n) we are able to define the spt-crank purely in terms of marked overpartitions. The proofs of the congruences depend on Bailey's Lemma and the difference formulas for the Dyson rank of an overpartition and the M2-rank of a partition without repeated odd parts.

The url of this page is http://qseries.org/fgarvan/abstracts/spt-overpartition-crank.html.
Created by F.G. Garvan (fgarvan@ufl.edu) on Sunday, November 17, 2013.
Last update made Tue Jul 8 16:55:48 EDT 2014.

fgarvan@ufl.edu