Introduction to symmetric functions and their combinatorics
Egge, Eric S.
Introduction to symmetric functions and their combinatorics - Providence, Rhode Island: American Mathematical Society, 2019. - xiii, 342p.; pbk; 22cm - Student mathematical library; Vol. 91 .
Includes bibliography and index
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 ω; 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.
https://bookstore.ams.org/stml-91/
9781470448998
Symmetric functions
Combinatorial analysis
Symmetric polynomials
Binomial coefficient
515.22 / EGG
Introduction to symmetric functions and their combinatorics - Providence, Rhode Island: American Mathematical Society, 2019. - xiii, 342p.; pbk; 22cm - Student mathematical library; Vol. 91 .
Includes bibliography and index
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 ω; 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.
https://bookstore.ams.org/stml-91/
9781470448998
Symmetric functions
Combinatorial analysis
Symmetric polynomials
Binomial coefficient
515.22 / EGG
