A Centralizer, Algebra Approach to Computing the Chromatic Polynomial

Date of Award

2004

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Poimenidou, Eirini

Keywords

Chromatic Polynomial, Graph Theory, Centralizer Algebra

Area of Concentration

Mathematics

Abstract

The recent research of Biggs, Klin, Pech, and Reinfeld in [2], [3], [5], [8] develop the general features of an innovative approach to computing the chromatic polynomial of a simple graph by examining the action of the symmetric group on the set of its proper colorings. The aim of this paper is, in part, to provide the general reader with a formal exposition of this method. The other goal of this work is to extend the scope of their approach by relating the basis elements of the centralizer algebra used by Klin and Pech [8] to the deletion-contraction method. The application of the representation theory of the symmetric group suggests a simplified approach which leads to a generalization of the well-known quasiseparation formula and equivalence class modelled by trees.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

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