Undergraduate Texts in Mathematics

Algebraic Combinatorics

Walks, Trees, Tableaux, and More

Authors: Stanley, Richard P.

  • Includes a new chapter on combinatorial commutative algebra 
  • First text on algebraic combinatorics targeted towards undergraduates
  • Written by the most well-known algebraic combinatorist world-wide
  • Covers topics of Walks in graphs, cubes and Radon transform, Matrix-Tree Theorem, the Sperner property, and more
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eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-77173-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $54.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: July 17, 2018
  • ISBN 978-3-319-77172-4
  • Free shipping for individuals worldwide
About this Textbook

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.

The new edition contains a bit more content than intended for a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Instructors may pick and choose chapters/sections for course inclusion and students can immerse themselves in exploring additional gems once the course has ended. A chapter on combinatorial commutative algebra (Chapter 12) is the heart of added material in this new edition. The author gives substantial application without requisites needed for algebraic topology and homological algebra. A sprinkling of additional exercises and a new section (13.8) involving commutative algebra, have been added.

From reviews of the first edition:

“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

About the authors

Richard P. 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.

Video

Table of contents (13 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-77173-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $54.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: July 17, 2018
  • ISBN 978-3-319-77172-4
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Combinatorics
Book Subtitle
Walks, Trees, Tableaux, and More
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-77173-1
DOI
10.1007/978-3-319-77173-1
Hardcover ISBN
978-3-319-77172-4
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XVI, 263
Number of Illustrations and Tables
87 b/w illustrations
Topics