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An Introduction to Symmetric Functions and Their Combinatorics

Eric S. Egge Carleton College, Northfield, MN
Available Formats:
Softcover ISBN: 978-1-4704-4899-8
Product Code: STML/91
List Price: $55.00 Individual Price:$44.00
Electronic ISBN: 978-1-4704-5493-7
Product Code: STML/91.E
List Price: $55.00 Individual Price:$44.00
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List Price: $82.50 Click above image for expanded view An Introduction to Symmetric Functions and Their Combinatorics Eric S. Egge Carleton College, Northfield, MN Available Formats:  Softcover ISBN: 978-1-4704-4899-8 Product Code: STML/91  List Price:$55.00 Individual Price: $44.00  Electronic ISBN: 978-1-4704-5493-7 Product Code: STML/91.E  List Price:$55.00 Individual Price: $44.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$82.50
• Book Details

Student Mathematical Library
Volume: 912019; 342 pp
MSC: Primary 05;

This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution $\omega$; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results.

The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.

Readership

Undergraduate and graduate students interested in algebra and combinatorics.

• Table of Contents

• Chapters
• Symmetric polynomials, the monomial symmetric polynomials, and symmetric functions
• The elementary, complete homogeneous, and power sum symmetric functions
• Interlude: Evaluations of symmetric functions
• Schur polynomials and Schur functions
• Interlude: A Rogues’ gallery of symmetric functions
• The Jacobi–Trudi identities and an involution on $\Lambda$
• The Hall inner product
• The Robinson–Schensted–Knuth correspondence
• Special products involving Schur functions
• The Littlewood–Richardson rule
• Linear algebra
• Partitions
• Permutations
• Additional Material

• Reviews

• This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi-Trudi identities; the involution ww; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan-Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood-Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples.

Anthony Mendesm, Cal Poly San Luis Obispo, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 912019; 342 pp
MSC: Primary 05;

This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution $\omega$; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results.

The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.

Readership

Undergraduate and graduate students interested in algebra and combinatorics.

• Chapters
• Symmetric polynomials, the monomial symmetric polynomials, and symmetric functions
• The elementary, complete homogeneous, and power sum symmetric functions
• Interlude: Evaluations of symmetric functions
• Schur polynomials and Schur functions
• Interlude: A Rogues’ gallery of symmetric functions
• The Jacobi–Trudi identities and an involution on $\Lambda$
• The Hall inner product
• The Robinson–Schensted–Knuth correspondence
• Special products involving Schur functions
• The Littlewood–Richardson rule
• Linear algebra
• Partitions
• Permutations
• This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi-Trudi identities; the involution ww; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan-Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood-Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples.

Anthony Mendesm, Cal Poly San Luis Obispo, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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