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The Symmetric Group

Representations, Combinatorial Algorithms, and Symmetric Functions
BuchGebunden
240 Seiten
Englisch
Springererschienen am20.04.20012nd ed.
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. Finally, we discuss Stanley's symmetric function analogue of the chromatic polynomial of a graph (Stn 95, Stn ta].mehr
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Produkt

KlappentextThis 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. Finally, we discuss Stanley's symmetric function analogue of the chromatic polynomial of a graph (Stn 95, Stn ta].
Details
ISBN/GTIN978-0-387-95067-9
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2001
Erscheinungsdatum20.04.2001
Auflage2nd ed.
ReiheGraduate Texts in Mathematics
Seiten240 Seiten
SpracheEnglisch
Gewicht549 g
IllustrationenXVI, 240 p.
Artikel-Nr.10504674

Inhalt/Kritik

Inhaltsverzeichnis
1 Group Representations.- 2 Representations of the Symmetric Group.- 3 Combinatorial Algorithms.- 4 Symmetric Functions.- 5 Applications and Generalizations.mehr
Kritik
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)mehr

Autor

There has recently been a resurgence of interest in representations of symmetric groups as well as other Coxeter groups. This book brings together for the first time many of the important results in this field. It includes a new chapter on applications of the materials from the first edition. The only prerequisites are elementary group theory and linear algebra.
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Sagan, Bruce E.