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Graduate Texts in Mathematics

The Symmetric Group

Representations, Combinatorial Algorithms, and Symmetric Functions

Authors: Sagan, Bruce

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About this Textbook

I have been very gratified by the response to the first edition, which has resulted in it being sold out. This put some pressure on me to come out with a second edition and now, finally, here it is. The original text has stayed much the same, the major change being in the treatment of the hook formula which is now based on the beautiful Novelli-Pak-Stoyanovskii bijection (NPS 97]. I have also added a chapter on applications of the material from the first edition. This includes Stanley's theory of differential posets (Stn 88, Stn 90] and Fomin's related concept of growths (Fom 86, Fom 94, Fom 95], which extends some of the combinatorics of Sn-representations. Next come a couple of sections showing how groups acting on posets give rise to interesting representations that can be used to prove unimodality results (Stn 82]. Finally, we discuss Stanley's symmetric function analogue of the chromatic polynomial of a graph (Stn 95, Stn ta]. I would like to thank all the people, too numerous to mention, who pointed out typos in the first edition. My computer has been severely reprimanded for making them. Thanks also go to Christian Krattenthaler, Tom Roby, and Richard Stanley, all of whom read portions of the new material and gave me their comments. Finally, I would like to give my heartfelt thanks to my editor at Springer, Ina Lindemann, who has been very supportive and helpful through various difficult times.

Reviews

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)


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-1-4757-6804-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-0-387-95067-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $69.99
price for USA in USD
  • ISBN 978-1-4419-2869-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Symmetric Group
Book Subtitle
Representations, Combinatorial Algorithms, and Symmetric Functions
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
203
Copyright
2001
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-6804-6
DOI
10.1007/978-1-4757-6804-6
Hardcover ISBN
978-0-387-95067-9
Softcover ISBN
978-1-4419-2869-6
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XVI, 240
Additional Information
Originally published by Wadsworth, Inc., 1991
Topics

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