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© 2013

Algebraic Combinatorics

Walks, Trees, Tableaux, and More

Textbook

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

  1. 1.(MIT), Dept. MathematicsMassachusetts Institute of TechnologyCambridgeUSA

About the authors

Professor Richard Stanley is one of the most well-known algebraic combinatorists in the world. He is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Amongst his several visiting professorships, Stanley has received numerous awards including the George Polya Prize in Applied Combinatorics, Guggenheim Fellowship, admission to both the American Academy and National Academies of Sciences, Leroy P. Steele Prize for Mathematical Exposition, Rolf Schock Prize in Mathematics, Senior Scholar at Clay Mathematics Institute, Aisenstadt Chair, Honorary Doctor of Mathematics from the University of Waterloo, and an honorary professorship at the Nankai University. Professor Stanley has had over 50 doctoral students and is well known for his excellent teaching skills. Stanley’s list of publications amount to over 155.

Bibliographic information

  • Book Title Algebraic Combinatorics
  • Book Subtitle Walks, Trees, Tableaux, and More
  • Authors Richard P. Stanley
  • Series Title Undergraduate Texts in Mathematics
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-6997-1
  • Softcover ISBN 978-1-4899-9285-7
  • eBook ISBN 978-1-4614-6998-8
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XII, 223
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Combinatorics
    Graph Theory
  • Buy this book on publisher's site

Reviews

“The chosen topics represent a sample of enumerative combinatorics suitable for the elementary algebra available to an undergraduate student. … This is a book that can be used to teach a topics course for senior undergraduates. It will help them to solidify their just-acquired abstract algebra and at the same it will introduce them to some beautiful topics in pure or applied combinatorics.” (Felipe Zaldivar, MAA Reviews, maa.org, December, 2015)

“This gentle book provides the perfect stepping-stone up. The various chapters treat diverse topics … . Stanley’s emphasis on ‘gems’ unites all this--he chooses his material to excite students and draw them into further study. … Summing Up: Highly recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 51 (8), April, 2014)