The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions: 203 (Graduate Texts in Mathematics, 203) - Hardcover

Sagan, Bruce E.

Hardcover

ISBN 10: 0387950672 ISBN 13: 9780387950679

Publisher: Springer, 2001

Synopsis

This book brings together many of the important results in this field.

From the reviews: ""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." --ZENTRALBLATT MATH

About this title

Review

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)

Synopsis

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 presentation is relaxed yet rigorous and the prerequisites 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 this field. On the other hand, a number of the combinatorial results presented 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 beautiful Novelli-Pak-Stoyanovskii proof of the hook formula (the latter being new to the second edition). In addition, there is a new chapter on applications of materials from the first edition.

Bruce Sagan is Professor of Mathematics at Michigan State University and has authored over 50 papers in combinatorics and its relation to algebra and topology. When he is not proving theorems, he is playing folk music from Scandinavian and the Balkans on the fiddle and its ethnic relatives.

Edition details

• Publisher: Springer
• Publication date: 2001
• ISBN 10: 0387950672
• ISBN 13: 9780387950679
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 256