Algebraic Combinatorics

Walks, Trees, Tableaux, and More

  • Richard P. Stanley

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Richard P. Stanley
    Pages 1-9
  3. Richard P. Stanley
    Pages 11-19
  4. Richard P. Stanley
    Pages 21-30
  5. Richard P. Stanley
    Pages 31-41
  6. Richard P. Stanley
    Pages 43-55
  7. Richard P. Stanley
    Pages 57-73
  8. Richard P. Stanley
    Pages 75-101
  9. Richard P. Stanley
    Pages 103-133
  10. Richard P. Stanley
    Pages 135-150
  11. Richard P. Stanley
    Pages 151-161
  12. Richard P. Stanley
    Pages 163-185
  13. Richard P. Stanley
    Pages 187-207
  14. Back Matter
    Pages 209-223

About this book

Introduction

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 knowledge to mathematical, engineering, and business models.

 

The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory.  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, and the Sperner property. 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.

 

Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Pólya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhäuser.

Keywords

Matrix-Tree Theorem Radon transform Sperner property algebraic combinatorics

Authors and affiliations

  • Richard P. Stanley
    • 1
  1. 1.(MIT), Dept. MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-6998-8
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-6997-1
  • Online ISBN 978-1-4614-6998-8
  • Series Print ISSN 0172-6056
  • About this book