The Symmetric Group:Representations, Combinatorial Algorithms, and Symmetric Functions (Wadsworth Series in Computer Information Systems) [Hardcover]

Bruce E. Sagan (Author)

Book Description

Publication Date: February 28, 1991 | ISBN-10: 0534155405 | ISBN-13: 978-0534155407 | Edition: 1

This book should be of interest to graduates.

Editorial Reviews

Review

From the reviews of the second edition: "This work is an introduction to the representation theory of the symmetric group. Unlike other books on the subject this text deals with the symmetric group from three different points of view: general representation theory, combinatorial algorithms and symmetric functions. ... This book is a digestible text for a graduate student and is also useful for a researcher in the field of algebraic combinatorics for reference." (Attila Maróti, Acta Scientiarum Mathematicarum, Vol. 68, 2002) "A classic gets even better. ... The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." (David M. Bressoud, Zentralblatt MATH, Vol. 964, 2001) --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 197 pages
• Publisher: Springer; 1 edition (February 28, 1991)
• Language: English
• ISBN-10: 0534155405
• ISBN-13: 978-0534155407
• Product Dimensions: 9.5 x 6.8 x 0.5 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 4.8 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #6,020,501 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

12 of 12 people found the following review helpful:

4.0 out of 5 stars Near Perfect, April 5, 2003

By 

Ross Mortensen (Kingston, Queensland Australia) - See all my reviews

This review is from: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Second Edition (Graduate Texts in Mathematics) (Hardcover)

This book is excellent. The material is presented clearly and concisely. It makes the subject matter accessible and interesting. I used it as the text for a one-semester graduate subject. I completed all of the exercises, so it is well-paced for this kind of study. I started with only an introductory knowledge of group theory, so it is self-contained. The only drawback is that there are no solutions to any of the exercises. If it had this, it would be a perfect bok.

9 of 9 people found the following review helpful:

5.0 out of 5 stars Worth the price just for the first chapter, February 7, 2007

By 

Peter J. Curry "darf_ferrara" (Charleston, SC) - See all my reviews
(REAL NAME)   

This review is from: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Second Edition (Graduate Texts in Mathematics) (Hardcover)

Sagans book makes representation theory easy. The book first covers representations using modules and then choosing a basis to show the matrix approach. With every new topic he develops it using what Doron Zeilberger has dubbed the Gelfand Principle ([...]) The principle is: "Always chooses the smallest example to make a point". It isn't easy to find the smallest example when Sn grows as quickly as it does, but Sagen always manages to do it.

The ensuing chapters follow in the same vein. Ideas are introduced and explained, sometimes with pictures, sometimes with calculations, but always as clearly as can be.

To read this book does require a firm grounding in linear algebra, as well as abstract algebra. Time reading it is time well spent.

7 of 10 people found the following review helpful:

5.0 out of 5 stars Good introduction for representation theory., March 24, 2000

By 

Kenei SUZUKI (Tokyo,Japan) - See all my reviews

This review is from: The Symmetric Group:Representations, Combinatorial Algorithms, and Symmetric Functions (Wadsworth Series in Computer Information Systems) (Hardcover)

This book has 4 chapters.Chapter1 is about general theory of representations of finite group.Chapter2 is about representation of symmetric groups.chapter3 and 4 are about combinatorial topics and symmetric functions. Though I haven't read all of the book,I highly recommand this book because this book shows us introductive part of representation theory with easy words.I think it is worth to read for all who are to begin the study of representation theory.