DATE: Tuesday, February 9 (2010), at 4:05pm
PLACE: LIT 305
SPEAKER: Krishnaswami Alladi
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TITLE:
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A fundamental invariant in the theory of partitions
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ABSTRACT:
Conjugation of Ferrers graphs is often used to
better undertstand the structure of various sets of partitions
in order to compute their generating functions. One important
invariant under conjugation is the number of different parts,
but this invariance has not been fully exploited. We will show
how this invariance can be used to give a transparent proof
of Cauchy's identity (=q-binomial theorem) and will obtain a
variant of Cauchy's identity in this process. This approach
will then be used to obtain a six parameter generalization of
Hiene's fundamental transformation motivated by Andrews'
combinatorial proof of a symmetric version of Hiene's transformation.
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