<P>This book brings together many of the important results in this field. </P> <P>From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanleyβs proof of the sum of squares formula using differentia
The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions
β Scribed by Bruce E. Sagan (auth.)
- Publisher
- Springer-Verlag New York
- Year
- 2001
- Tongue
- English
- Leaves
- 257
- Series
- Graduate Texts in Mathematics 203
- Edition
- 2
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
β¦ Table of Contents
Front Matter....Pages i-xv
Group Representations....Pages 1-51
Representations of the Symmetric Group....Pages 53-89
Combinatorial Algorithms....Pages 91-140
Symmetric Functions....Pages 141-190
Applications and Generalizations....Pages 191-222
Back Matter....Pages 223-241
β¦ Subjects
Group Theory and Generalizations; Combinatorics
π SIMILAR VOLUMES
This text is an introduction to the representation theory of the symmetric group from three different points of view: via general representation theory, via combinatorial algorithms, and via symmetric functions. It is the only book to deal with all three aspects of this subject at once. The style of
<P>This book brings together many of the important results in this field. </P> <P>From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanleyβs proof of the sum of squares formula using differentia
Summer research report, expository. Version 28, Aug 2019