Rectification of Composition Tableaux

TL;DR

This paper introduces an algorithm for rectifying cells in composition tableaux and generalizes it to handle multiple bottom-justified cells in the first column, expanding the applicability of tableau rectification techniques.

Contribution

It presents a novel rectification algorithm for composition tableaux and extends it to multiple cells, enhancing the flexibility of tableau transformations.

Findings

Algorithm successfully rectifies individual cells in composition tableaux.

Generalization allows rectification of multiple bottom-justified cells.

Potential applications in algebraic combinatorics and tableau theory.

Abstract

In this paper 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.