Plancherel Averages: Remarks on a Paper by Stanley

Source abstract

Let $M_n$ stand for the Plancherel measure on ${\Bbb Y}_n$, the set of Young diagrams with $n$ boxes. A recent result of R. P. Stanley (arXiv: 0807.0383) says that for certain functions $G$ defined on the set ${\Bbb Y}$ of all Young diagrams, the average of $G$ with respect to $M_n$ depends on $n$ polynomially. We propose two other proofs of this result together with a generalization to the Jack deformation of the Plancherel measure.