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About this book
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.
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Table of contents (5 chapters)
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)
Authors and Affiliations
Bibliographic Information
Book Title: The Symmetric Group
Book Subtitle: Representations, Combinatorial Algorithms, and Symmetric Functions
Authors: Bruce E. Sagan
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4757-6804-6
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2001
Hardcover ISBN: 978-0-387-95067-9Published: 20 April 2001
Softcover ISBN: 978-1-4419-2869-6Published: 01 December 2010
eBook ISBN: 978-1-4757-6804-6Published: 09 March 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 2
Number of Pages: XVI, 240
Additional Information: Originally published by Wadsworth, Inc., 1991