06240 - The Symmetric Group - Representations, Combinatorial Algorithms, and Symmetric Functions [Sagan].pdf

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Graduate
Texts
in
Mathematics
Bruce E. Sagan
The Symmetric
Group
Representations,
Combinatorial
Algorithms, and
Symmetric Functions
Graduate Texts in Mathematics
203
S. Axler
Editorial Board
F.W. Gehring K.A. Ribet
Springer
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TAKEUTIIZARING. Introduction to
Axiomatic Set Theory. 2nd ed.
OXTOBY. Measure and Category. 2nd ed.
SCHAEFER. Topological Vector Spaces.
2nd ed.
HIL TON/ST AMMBACH. A Course in
Homological Algebra. 2nd ed.
MAC LANE. Categories for the Working
Mathematician. 2nd ed.
HuGHES/PIPER. Projective Planes.
SERRE. A Course in Arithmetic.
TAKEUTI/ZARING. Axiomatic Set Theory.
HUMPHREYS. Introduction to Lie Algebras
and Representation Theory.
CoHEN. A Course in Simple Homotopy
Theory.
CoNWAY. Functions of One Complex
Variable I. 2nd ed.
BEALS. Advanced Mathematical Analysis.
ANDERSON/FULLER. Rings and Categories
of Modules. 2nd ed.
GoLUBITSKY/GuiLLEMIN. Stable Mappings
and Their Singularities.
BERBERIAN. Lectures in Functional
Analysis and Operator Theory.
WINTER. The Structure of Fields.
RosENBLATT. Random Processes. 2nd ed.
HALMOS. Measure Theory.
HALMOS. A Hilbert Space Problem Book.
2nd ed.
HUSEMOLLER. Fibre Bundles. 3rd ed.
HUMPHREYS. Linear Algebraic Groups.
BARNES/MACK. An Algebraic Introduction
to Mathematical Logic.
GREUB. Linear Algebra. 4th ed.
HOLMES. Geometric Functional Analysis
and Its Applications.
HEWITT/STROMBERG. Real and Abstract
Analysis.
MANES. Algebraic Theories.
KELLEY. General Topology.
ZARISKIISAMUEL. Commutative Algebra.
Vol. I.
ZARISKI/SAMUEL. Commutative Algebra.
Vol. II.
JACOBSON. Lectures in Abstract Algebra
I.
Basic Concepts.
JACOBSON. Lectures in Abstract Algebra II.
Linear Algebra.
JACOBSON. Lectures in Abstract Algebra
III. Theory of Fields and Galois Theory.
HIRSCH. Differential Topology.
SPITZER. Principles of Random Walk.
2nd ed.
ALEXANDERIWERMER. Several Complex
Variables and Banach Algebras. 3rd ed.
36 KELLEYINAMIOKA et al. Linear
Topological Spaces.
37 MONK. Mathematical Logic.
38 GRAUERTIFRITZSCHE. Several Complex
Variables.
39 ARVESON. An Invitation to C*-Algebras.
40 KEMENY/SNELL/KNAPP. Denumerable
Markov Chains. 2nd ed.
41 APOSTOL. Modular Functions and Dirichlet
Series in Number Theory.
2nd ed.
42 SERRE. Linear Representations of Finite
Groups.
43 GILLMAN/JERISON. Rings of Continuous
Functions.
44 KENDIG. Elementary Algebraic Geometry.
45 LOEVE. Probability Theory
I.
4th ed.
46 LOEVE. Probability Theory II. 4th ed.
47 MoiSE. Geometric Topology in
Dimensions 2 and 3.
48 SACHS/Wu. General Relativity for
Mathematicians.
49 GRUENBERG/WEIR. Linear Geometry.
2nd ed.
50 EDWARDS. Fermat's Last Theorem.
51 KLINGENBERG. A Course in Differential
Geometry.
52 HARTSHORNE. Algebraic Geometry.
53 MANIN. A Course in Mathematical Logic.
54 GRA VERIW ATKINS. Combinatorics with
Emphasis on the Theory of Graphs.
55 BROWN/PEARCY. Introduction to Operator
Theory I: Elements of Functional
Analysis.
56 MASSEY. Algebraic Topology: An
Introduction.
57 CROWELL/Fox. Introduction to Knot
Theory.
58 KOBLITZ. p-adic Numbers, p-adic Analysis,
and Zeta-Functions. 2nd ed.
59 LANG. Cyclotomic Fields.
60 ARNOLD. Mathematical Methods in
Classical Mechanics. 2nd ed.
61 WHITEHEAD. Elements of Homotopy
Theory.
62 KARGAPOLOV /MERLZJAKOV. Fundamentals
ofthe Theory of Groups.
63 BOLLOBAS. Graph Theory.
64 EDWARDS. Fourier Series. Vol.
I.
2nd ed.
65 WELLS. Differential Analysis on Complex
Manifolds. 2nd ed.
35
(continued after index)
Bruce E. Sagan
The Symmetric Group
Representations, Combinatorial
Algorithms, and Symmetric Functions
Second Edition
With 31 Figures
Bruce E. Sagan
Department of Mathematics
Michigan State University
East Lansing, MI 48824-1027
USA
Editorial Board
S. Axler
Mathematics Department
San Francisco State
University
San Francisco, CA 94132
USA
F.W. Gehring
Mathematics Department
East Hall
University of Michigan
Ann Arbor, MI 48109
USA
K.A. Ribet
Mathematics Department
University of California
at Berkeley
Berkeley, CA 94 720-3840
USA
Mathematics Subject Classification (2600): 20Cxx, 20C30, 20C32, 05C85
Library of Congress Cataloging-in-Publication Data
Sagan, Bruce Eli.
The symmetric group : representations, combinatorial algorithms, and symmetric
functions
I
Bruce E. Sagan.
p. em. -(Graduate texts in mathematics ; 203)
Includes bibliographical references and index.
ISBN 0-387-95067-2 (alk. paper)
1. Representations of groups. 2. Symmetric functions. I. Title. II. Series.
QA171 .S24 2000
00-040042
512· .2-dc21
Printed on acid-free paper.
First edition
©
1991 by Wadsworth, Inc., Belmont, California.
©
2001 Springer-Verlag New York, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York,
NY 100
I
0, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use
in connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the
former are not especially identified, is not to be taken as a sign that such names, as understood by
the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
Production managed by Timothy Taylor; manufacturing supervised by Jeffrey Taub.
Photocomposed copy prepared from
th~
author's LaTeX files.
Printed and bound by Edwards Bvothers, ,Jnc., Ann Arbor, MI.
Printed in the United
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