Dyson's Rank Function and Andrews' SPT Function

Abstract: 

Let spt(n) denote the number of smallest parts in the partitions of n. In 2008, Andrews found surprising congruences for the spt-function mod 5, 7 and 13. We discuss new congruences for spt(n) mod powers of 2. We give new generating function identities for the spt-function and Dyson's rank function. Recently with Andrews and Liang we found a spt-crank function that explains Andrews spt-congruences mod 5 and 7. We extend these results by finding spt-cranks for various overpartition-spt-functions of Ahlgren, Bringmann, Lovejoy and Osburn. This most recent work is joint with Chris Jennings-Shaffer.

(This seminar will be viewed via Access Grid. The host institution is The University of Newcastle.)