CARMA OANT SEMINAR Speaker: Prof Frank Garvan, University of Florida Title: Dyson's Rank Function and Andrews's SPT Function. Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: CARMA [ENQUIRIES] Time and Date: 3:00 pm, Tue, 20th Aug 2013 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. [Permanent link]