An Introduction to Symmetric Functions and Their Combinatorics

Eric S. Egge

ISBN 10: 1470448998 / ISBN 13: 9781470448998

Published by American Mathematical Society, US, 2019

About this Item

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.

Seller Inventory # LU-9781470448998

Bibliographic Details

• Title: An Introduction to Symmetric Functions and Their Combinatorics
• Publisher: American Mathematical Society, US
• Publication Date: 2019
• Language: English
• ISBN 10: 1470448998
• ISBN 13: 9781470448998
• Binding: Paperback
• Condition: New

About this title

Synopsis

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 ; 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.

About the Author

Eric S. Egge: Carleton College, Northfield, MN