© 2018

Algebraic Combinatorics

Walks, Trees, Tableaux, and More


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

Table of contents

  1. Front Matter
    Pages i-xvi
  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 31-42
  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 151-162
  12. Richard P. Stanley
    Pages 163-185
  13. Richard P. Stanley
    Pages 187-217
  14. Richard P. Stanley
    Pages 219-244
  15. Back Matter
    Pages 245-263

About this book


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


Matrix-Tree Theorem Radon transform Sperner property algebraic combinatorics textbook adopt algebraic combinatorics undergraduate algebraic combinatorics walks in graphs combinatorial commutative algebra Eulerian digraphs RSK algorithm Young tableaux plane partitions Sperner property random walks radon transform planar graphs simplicial complexes Fisher inequality Hadamard matrices affine monoids

Authors and affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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.

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
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-77172-4
  • Softcover ISBN 978-3-030-08389-2
  • eBook ISBN 978-3-319-77173-1
  • Series ISSN 0172-6056
  • Series E-ISSN 2197-5604
  • Edition Number 2
  • Number of Pages XVI, 263
  • Number of Illustrations 87 b/w illustrations, 0 illustrations in colour
  • Topics Combinatorics
    Graph Theory
  • Buy this book on publisher's site