Polynomials associated with graph coloring and orientations

Title Page Abstract Table of Contents List of Figures Introduction Background Posets Formal Power Series Partitions and Compositions Symmetric and Quasisymmetric Functions Graphs Definitions Orientations Graph Colorings and the Tutte Polynomial Hopf algebras Algebras and Coalgebras Bialgebras and Hopf Algebras Combinatorial Hopf Algebras The k-chromatic Quasisymmetric Function of a Graph Definitions L-positivity XkG on Special Classes of Graphs Cycles Complete bipartite graphs The k-balanced Chromatic Polynomial Further Questions The Graph Hopf Algebra Definitions An Alternate Antipode Formula Inversion of Characters Tutte characters The Polynomial Associated to the Rank-Nullity Character Applications to Tutte Polynomial Evaluations Further Questions Maple Routines for Calculating XGk Bibliography