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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-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

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 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

Keywords

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

  • Richard P. Stanley
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-77173-1
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-77172-4
  • Online ISBN 978-3-319-77173-1
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • Buy this book on publisher's site