Title
The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions (Graduate Texts in Mathematics, Vol. 203,Used
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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 NovelliPakStoyanovskii 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 Snrepresentations. 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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- Q: What is the main focus of 'The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions'? A: The book focuses on the theory of symmetric groups, exploring their representations, combinatorial algorithms, and symmetric functions, aiming to provide comprehensive insights into these mathematical concepts.
- Q: Who is the author of this book? A: The author of the book is Bruce E. Sagan, who is known for his contributions to combinatorics and algebra.
- Q: What are the key updates in the second edition of this book? A: The second edition includes a revised treatment of the hook formula based on the Novelli-Pak-Stoyanovskii bijection and adds a chapter on applications related to differential posets and growths.
- Q: How many pages does the book contain? A: The book contains 256 pages, providing a detailed exploration of its subject matter.
- Q: What is the binding type of this book? A: This book is available in hardcover binding, offering durability for long-term use.
- Q: Is this book suitable for beginners in mathematics? A: While the book is comprehensive, it is best suited for readers with a background in mathematics, particularly those familiar with combinatorics and group theory.
- Q: When was the second edition of this book published? A: The second edition was published on April 20, 2001.
- Q: What topics are covered in the additional chapter of the second edition? A: The additional chapter covers applications related to Stanley's theory of differential posets and Fomin's growths, extending the combinatorial aspects of symmetric group representations.
- Q: What is the item condition of this book? A: The item condition of this book is 'New', indicating it has not been previously owned or used.
- Q: Can this book be useful for research purposes? A: Yes, this book is a valuable resource for researchers and students interested in the advanced topics of symmetric groups and their applications in mathematics.