Representations, Combinatorial Algorithms, and Symmetric Functions
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 minimumAundergraduate courses in linear algebra and group theory will suffice.From the reviews of the second edition:pThis 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 MarA3ti, Acta Scientiarum Mathematicarum, Vol. 68, 2002)pA classic gets even better. … The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanleya (TM)s proof of the sum of squares formula using differential posets, Fomina (TM)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)