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An Introduction to Symmetric Functions and Their Combinatorics
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-4899-8 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4899-8 (ISBN)
Offers a reader-friendly introduction to the theory of symmetric functions. It includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases. The prerequisites for the book are minimal-familiarity with linear algebra, partitions, and generating functions.
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.
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.
Eric S. Egge, Carleton College, Northfield, MN.
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
Bibliography
Index
Erscheinungsdatum | 03.01.2020 |
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Reihe/Serie | Student Mathematical Library |
Verlagsort | Providence |
Sprache | englisch |
Maße | 140 x 216 mm |
Gewicht | 440 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
Mathematik / Informatik ► Mathematik ► Graphentheorie | |
ISBN-10 | 1-4704-4899-8 / 1470448998 |
ISBN-13 | 978-1-4704-4899-8 / 9781470448998 |
Zustand | Neuware |
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