Symmetric Functions: A Beginner's Course

Preface
Contents
Part I Schur Polynomials and Young Tableaux
	Chapter 1 Symmetric Polynomials
		1.1 Definition and First Examples
		1.2 The Fundamental Theorem of Symmetric Polynomials
		1.3 Complete Symmetric Polynomials
		1.4 Generating Functions
		1.5 Newton Power Sums
		1.6 Bases and Partitions
		1.7 More About Partitions
		1.8 Monomial Symmetric Polynomials
		1.9 Problems
	Chapter 2 Schur Polynomials
		2.1 Skew-Symmetric Polynomials
		2.2 Schur Polynomials
		2.3 The First Jacobi–Trudi Identity
		2.4 The Pieri Formulas
		2.5 Problems
	Chapter 3 Combinatorial Formula for Schur Polynomials
		3.1 Young Tableaux
		3.2 Noncrossing Paths
		3.3 The Case of Two Paths
		3.4 The General Case
		3.5 The Lindström–Gessel–Viennot Lemma
		3.6 Problems
	Chapter 4 The Ring of Symmetric Functions
		4.1 The Cauchy Product
		4.2 Ring of Symmetric Functions as the Projective Limit of