Constructive Method for Finding the Coefficients of a Divided Symmetrization

Abstract

We consider a type of divided symmetrization ${\overrightarrow{D}}_{\lambda ,G}$ where $\lambda$ is a nonincreasing partition on $n$ and where $G$ is a graph. We discover that in the case where $\lambda$ is a hook shape partition with first part equal to 2, we may determine the expansion of ${\overrightarrow{D}}_{\lambda ,G}$ over the basis of Schur functions. We show a combinatorial construction for finding the terms of the expansion and a second construction that allows computation of the coefficients.

15 pages

References in corpus (1)

• Explicit computations with the Divided Symmetrization operator