DATE: Tuesday, February 2 (2010), at 4:05pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
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A combinatorial proof and a new interpretation
of the Jacobi triple product identity for theta functions
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ABSTRACT:
Jacobi's triple product identity is one of the
most fundamental in the theory of theta functions and in
the theory of partitions and q-series. We will provide a
combinatorial proof by considering representations of
partitions in terms of 3-modular Ferrers graphs. Next we
will discuss a weighted partition theorem in three free
parameters connecting partitions into distinct parts and
partitions into parts that differ by at least 3. We will show
how Jacobi's triple product identity falls out as a special
case from this three parameter partition theorem.
TBA
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