SMS scnews item created by Andrew Mathas at Fri 16 Aug 2013 1848
Expiry: 20 Aug 2013
Calendar1: 20 Aug 2013 1500-1600
CalLoc1: AGR Seminar
CalTitle1: AGR Seminar: Dyson’s Rank Function and Andrews’s SPT Function
Auth: firstname.lastname@example.org in SMS-auth
Dyson’s Rank Function and Andrews’s SPT Function
Prof Frank Garvan, University of Florida
University of Newcastle (CARMA)
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.
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