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 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.
- Book Title Algebraic Combinatorics
- Book Subtitle Walks, Trees, Tableaux, and More
- 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
- Buy this book on publisher's site
“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)