Algebraic Combinatorics
eBook - ePub

Algebraic Combinatorics

  1. 368 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Algebraic Combinatorics

About this book

This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

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Yes, you can access Algebraic Combinatorics by Chris Godsil in PDF and/or ePUB format, as well as other popular books in Mathematics & Counting & Numeration. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Table of Contents
  7. Preface
  8. 1 The Matchings Polynomial
  9. 2 The Characteristic Polynomial
  10. 3 Formal Power Series and Generating Functions
  11. 4 Walk Generating Functions
  12. 5 Quotients of Graphs
  13. 6 Matchings and Walks
  14. 7 Pfaffians
  15. 8 Orthogonal Polynomials
  16. 9 Moment Sequences
  17. 10 Strongly Regular Graphs
  18. 11 Distance-Regular Graphs
  19. 12 Association Schemes
  20. 13 Representations of Distance-Regular Graphs
  21. 14 Polynomial Spaces
  22. 15 Q-Polynomial Spaces
  23. 16 Tight Designs
  24. Appendix: Terminology
  25. Index of Symbols
  26. Index