The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions / Edition 2

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This text is an introduction to the representation theory of the symme tric group from three different points of view: via general representa tion theory, via combinatorial algorithms, and via symmetric functions . It is the only book to deal with all three aspects of this subject a t once. The style of presentation is relaxed yet rigorous and the prer equisites have been kept to a minimum, undergraduate courses in linear algebra and group theory will suffice. And this is a very active area of current research, so the text will appeal to graduate students and mathematicians in other specialties interested in finding out about t his field. On the other hand, a number of the combinatorial results pr esented have never appeared in book form before and so the volume will serve as a good reference for teachers already working in this area. Among these results are Haiman's theory of dual equivalence and the be autiful Novelli-Pak-Stoyanovskii proof of the hook formula (the latter being new to the second edition).

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Editorial Reviews

From the Publisher

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)

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Product Details

  • ISBN-13: 9780387950679
  • Publisher: Springer New York
  • Publication date: 4/20/2001
  • Series: Graduate Texts in Mathematics Series, #203
  • Edition description: 2nd ed. 2001
  • Edition number: 2
  • Pages: 240
  • Product dimensions: 0.69 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

* Group Representations
• Representations of the Symmetric Group
• Combinatorial Algorithms
• Symmetric Functions
• Applications and Generalizations
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