Algebraic Combinatorics Walks, Trees, Tableaux, and More /

• Main Author: Stanley, Richard P. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Combinatorics.; Graph theory.; Graph Theory.

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebr...

Table of Contents:

• Preface
• Notation.- 1. Walks in graphs
• 2. Cubes and the Radon transform
• 3. Random walks
• 4. The Sperner property
• 5. Group actions on boolean algebras
• 6. Young diagrams and q-binomial coefficients
• 7. Enumeration under group action
• 8. A glimpse of Young tableaux
• Appendix. The RSK algorithm
• Appendix. Plane partitions
• 9. The Matrix–Tree Theorem
• Appendix. Three elegant combinatorial proofs
• 10. Eulerian diagraphs and oriented trees
• 11. Cycles, bonds, and electrical networks
• 12. Miscellaneous gems of algebraic combinatorics
• Hints
• References.