DATE:
Tuesday, July 26 (2011), at 11:00am
PLACE: LIT 368
SPEAKER:
Jie Liang (University of Central Florida)
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TITLE:
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Combinatorial refinements of Andrews' congruences for the
spt-function modulo 5 and 7
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ABSTRACT:
Let spt(n) denote to total number of smallest parts in the
partitions of n. Andrews proved
spt(5n + 4) = 0 (mod 5)
spt(7n + 5) = 0 (mod 7)
spt(13n + 6) = 0 (mod 13)
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
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