The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions

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Bruce E. Sagan

The Symmetric Group

Representations, Combinatorial Algorithms, and Symmetric Functions

Bruce E. Sagan

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English

Springer-Verlag New York Inc.
01 December 2010

Mathematics & Sciences; Discrete mathematics; Groups & group theory

Series: Graduate Texts in Mathematics

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.

By: Bruce E. Sagan
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of hardcover 2nd ed. 2001
Volume: 203
Dimensions: Height: 235mm, Width: 155mm, Spine: 13mm
Weight: 820g
ISBN: 9781441928696
ISBN 10: 1441928693
Series: Graduate Texts in Mathematics
Pages: 240
Publication Date: 01 December 2010
Audience: Professional and scholarly , Professional and scholarly , Undergraduate , Further / Higher Education
Format: Paperback
Publisher's Status: Active

1 Group Representations.- 2 Representations of the Symmetric Group.- 3 Combinatorial Algorithms.- 4 Symmetric Functions.- 5 Applications and Generalizations.

Reviews for The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions

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 Maroti, 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)