This is a course on the combinatorial theory of symmetric functions. We will develop the basic structure of the ring of symmetric functions, leading up to the study of Schur functions and the Littlewood-Richardson rule for multiplying them. In general, we will prefer combinatorial arguments, but we will also see occasional connections with geometry and representation theory. In the last segment of the course, we will explore connections with probability and computational complexity.
Classes are on Monday, Wednesday, and Friday, 3:00 - 3:55 pm, in Bolz 120.
As a main text, we will use Chapter 7 of Richard Stanley's Enumerative Combinatorics, Vol. 2. We will occasionally draw on other sources, including Macdonald's book, as well as recent research articles.
Grades will be based on several homework assignments.