Seminar information archive ~05/22Next seminarFuture seminars 05/23~


17:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Guoniu Han (Université de Strasbourg/CNRS)
Integer partitions and hook length formulas (ENGLISH)
[ Abstract ]
Integer partitions were first studied by Euler.
The Ferrers diagram of an integer partition is a very useful tool for
visualizing partitions. A Ferrers diagram is turned into a Young tableau
by filling each cell with a unique integer satisfying some conditions.
The number of Young tableaux is given by the famous hook length formula,
discovered by Frame-Robinson-Thrall.
In this talk, we introduce the hook length expansion technique and
explain how to find old and new hook length formulas for integer
partitions. In particular, we derive an expansion formula for the
powers of the Euler Product in terms of hook lengths, which is also
discovered by Nekrasov-Okounkov and Westburg. We obtain an extension
by adding two more parameters. It appears to be a discrete
interpolation between the Macdonald identities and the generating
function for t-cores. Several other summations involving hook length,
in particular, the Okada-Panova formula, will also be discussed.
[ Reference URL ]