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

Matjaz Konvalinka
Vanderbilt University

Monday, March 23, 2009
4:00 pm, 845 Patterson Office Tower

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.