Discrete CATS Seminar
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U N I V E R S I T Y O F K E N T U C K Y

DISCRETE
CATS
SEMINAR

WHERE CATS =
COMBINATORICS,
ALGEBRA,
TOPOLOGY
&
STATISTICS!

845 PATTERSON OFFICE TOWER

2008 - 2009

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"A bijective proof of a partition conjecture due to Ciocan"

Matjaz Konvalinka

Vanderbilt University

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Monday, March 23, 2009

4:00 pm, 845 Patterson Office Tower

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Abstract:

Recently, Ciocan posed a conjecture that states that a certain sum
over the squares of a Young diagram of a partition depends only on the
size of the partition. I will explain how to interpret this conjecture
as a polynomial identity over some commutative variables, and then
present a bijective proof of this identity. I will also give a
probabilistic interpretation of the result that is slightly
reminiscent of the Greene-Nijenhuis-Wilf proof of the hook length
formula. This is joint work with Ciocan and Pak.