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Egge's goal is to make the theory of symmetric functions more accessible to undergraduate students, taking a combinatorial approach wherever feasible, and showing both the core of the subject and some of the areas that are active today. He assumes students have completed introductory courses in linear algebra and combinatorics, but appends summaries of the ideas from those fields that he uses. The topics include symmetric polynomials, the monomial symmetric polynomials, and symmetric functions; Schur polynomials and Schur functions; the Jacobi-Trudi identities and an involution on A; the Hall inner product; and the Littlewood-Richardson rule. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)
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An Introduction to Symmetric Functions and Their Combinatorics
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American Mathematical Society, 2020
ISBN 10: 1470448998
ISBN 13: 9781470448998
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An Introduction to Symmetric Functions and Their Combinatorics
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ISBN 13: 9781470448998
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Paperback. Condizione: New. 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. Codice articolo LU-9781470448998
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An Introduction to Symmetric Functions and Their Combinatorics
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American Mathematical Society, US, 2019
ISBN 10: 1470448998
ISBN 13: 9781470448998
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Paperback. Condizione: New. 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. Codice articolo LU-9781470448998
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An Introduction to Symmetric Functions and Their Combinatorics (Student Mathematical Library)
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Condizione: New. 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, p. Codice articolo 604054987
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An Introduction to Symmetric Functions and Their Combinatorics
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Introduction to Symmetric Functions and Their Combinatorics
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ISBN 13: 9781470448998
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