DATE: Tuesday, February 23 (2010), at 4:05pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
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A new combinatorial proof of the Rogers-Fine identity
and a related partial theta series
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ABSTRACT:
This lecture can be considered as part II of my
earlier talk in the seminar on "A fundamental invariant in the
theory of partitions", but will be self contained. In this talk, by
exploiting the invariance of the number of different parts under
conjugation of Ferrers graphs, we will give the simplest and
most direct derivation of the Rogers-Fine identity. This approach
also provides a very nice combinatorial proof and explanation of
a certain partial theta identity which is a striking special case
of the Rogers-Fine identity.
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