Algebraic Combinatorics Walks Trees Tableaux and More 2nd Edition by Richard 9783319771724 3319771728

Algebraic Combinatorics Walks Trees Tableaux and More 2nd Edition Richard P Stanley – Ebook PDF Instant Download/Delivery ISBN: 9783319771724, 3319771728

Product details:

• ISBN 10:3319771728
• ISBN 13: 9783319771724
• Author: Richard

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 algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound understanding to mathematical, engineering, and business models. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, de Bruijn sequences, the Erdős–Moser conjecture, electrical networks, the Sperner property, shellability of simplicial complexes and face rings. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees.

Table Contents:

1. Cover
2. Front Matter
3. 1. Walks in Graphs
4. 2. Cubes and the Radon Transform
5. 3. Random Walks
6. 4. The Sperner Property
7. 5. Group Actions on Boolean Algebras
8. 6. Young Diagrams and q-Binomial Coefficients
9. 7. Enumeration Under Group Action
10. 8. A Glimpse of Young Tableaux
11. 9. The Matrix-Tree Theorem
12. 10. Eulerian Digraphs and Oriented Trees
13. 11. Cycles, Bonds, and Electrical Networks
14. 12. A Glimpse of Combinatorial Commutative Algebra
15. 13. Miscellaneous Gems of Algebraic Combinatorics
16. Back Matter

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