Rectification of Composition Tableaux

Abstract

In this thesis we define an algorithm for rectifying one cell in a composition tableau. We then describe a generalization of this rectification process. The generalization is from one cell in the first column to any number of cells in the first column, provided they are bottom-justified. We show this rectification of a composition tableau commutes with the rectification of a reverse semi-standard Young tableau. Rectification of reverse semi-standard Young tableaux is used to define evacuation of reverse semi-standard Young tableaux. We define evacuation for composition tableaux using our rectification process for composition tableaux.