DATE:
Tuesday, September 13 (2011), at 1:55pm
PLACE: LIT 368
SPEAKER:
Frank Garvan
|
TITLE:
|
Combinatorial Interpretations of Congruences for the
SPT-Function - Part 1
|
ABSTRACT:
Let spt(n) denote to total number of smallest parts in the
partitions of n. Andrews (2008) proved that
spt(5n + 4) = 0 (mod 5)
spt(7n + 5) = 0 (mod 7)
spt(13n + 6) = 0 (mod 13)
In Part 1,
we give a vector-partition type crank which refines the congruences
mod 5 and 7. Proofs depend on Bailey's Lemma and known results
for the rank and crank of partitions. This is joint work with
George Andrews and Jie Liang. This is a repeat of a talk given by
Jie Liang in the summer.
|