This book presents an introduction to some of the interactions between algebra and combinatorics. It focuses on the characteristic and matchings polynomials of a graph and introduces the theory of polynomial spaces. The book is intended for beginning graduate students in mathematics.
Table of Contents
1. The Matchings Polynomial 2. The Characteristic Polynomial 3. Formal Power Series and Generating Functions 4. Walk Generating Functions 5. Quotients of Graphs 6. Matchings and Walks 7. Pfaffians 8. Orthogonal Polynomials 9. Moment Sequences 10. Strongly Regular Graphs 11. Distance-Regular Graphs 12. Association Schemes 13. Representations of Distance-Regular Graphs 14. Polynomial Spaces 15. Q-Polynomial Spaces 16. Tight Designs
"The topics have been thoughtfully chosen and masterfully integrated into the text. The result is a delightfully entertaining and informative excursion into the field...this text provides the most comprehensive treatment I have encountered...this book is likely to become a permanent fixture in the study..."
- Mathematical Reviews