Egge E An introduction to symmetric functions combinatorics 2019 torrent

Textbook in PDF format

Contents:
Preface
Symmetric Polynomials, the Monomial Symmetric Polynomials, and Symmetric Functions
Symmetric Polynomials
The Monomial Symmetric Polynomials
Symmetric Functions
Problems
Notes
The Elementary, Complete Homogeneous, and Power Sum Symmetric Functions
The Elementary Symmetric Functions
The Complete Homogeneous Symmetric Functions
The Power Sum Symmetric Functions
Problems
Interlude: Evaluations of Symmetric Functions
Symmetric Function Identities
Binomial Coefficients
Stirling Numbers of the First and Second Kinds
q-Binomial Coefficients
Problems
Notes
Schur Polynomials and Schur Functions
Schur Functions and Semistandard Tableaux
Schur Polynomials as Ratios of Determinants
Problems
Notes
Interlude: A Rogues’ Gallery of Symmetric Functions
Skew Schur Functions
Stable Grothendieck Polynomials
Dual Stable Grothendieck Polynomials
The Chromatic Symmetric Function
Problems
Notes
The Jacobi–Trudi Identities and an Involution on
The First Jacobi–Trudi Identity
The Second Jacobi–Trudi Identity
The Involution
Problems
Notes
The Hall Inner Product
Inner Products on
The Hall Inner Product and Cauchy’s Formula
The Hall Inner Product on the Power Sum Symmetric Functions
Problems
Notes
The Robinson–Schensted–Knuth Correspondence
RSK Insertion: Constructing
Constructing
Implementing RSK with Growth Diagrams
Problems
Notes
Special Products Involving Schur Functions
The Pieri Rules
The Murnaghan–Nakayama Rule
Problems
The Littlewood–Richardson Rule
Products of Tableaux
Knuth Equivalence
The Relationship Between P and word
The Littlewood–Richardson Rule
Problems
Notes
Appendix A Linear Algebra
Fields and Vector Spaces
Bases and Linear Transformations
Inner Products and Dual Bases
Problems
Appendix B Partitions
Partitions and a Generating Function
Problems
Appendix C Permutations
Permutations as Bijections
Determinants and Permutations
Problems
Bibliography
Index