Dyson's Rank Function and Andrews's SPT Function

Host Institution:

University of Newcastle (CARMA)

Title of Seminar:

Dyson's Rank Function and Andrews's SPT Function

Speaker's Name:

Prof Frank Garvan

Speaker's Institution:

University of Florida

Time and Date:

Tuesday 20 August 2013, 3.00pm (AEST)

Seminar 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.

Seminar Convener:

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