Cornell Math - MATH 739, Fall 1999

MATH 739 — Fall 1999
Topics in Algebra

Instructor: Vesselin Gasharov

Time: WF 1:25-2:40

Room: Malott 206

This course will be an introduction to enumerative combinatorics and some of its connections with algebra. First we will introduce some of the basic notions in enumerative combinatorics, such as partitions, compositions, lattice paths, generating functions, posets, etc. Then we will explore the theory of symmetric functions. We will follow mainly Richard Stanley's new book Enumerative Combinatorics, volume 2, published by Cambridge University Press. Some of the topics that we will cover include the Robinson-Schensted-Knuth algorithm, the Littlewood-Richardson rule, the Jacobi-Trudi identity, the Jeu de Taquin. Time permitting, we will also cover some topics on Hilbert functions and h-vectors. We will discuss open problems and conjectures.