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.)
Speaker
Prof Frank Garvan (via Access Grid)
Research Area
Access Grid Seminar
Affiliation
University of Florida
Date
Tue, 20/08/2013 - 3:00pm
Venue
RC-4082, The Red Centre (via Access Grid from The University of Newcastle)