Cornell Math - MATH 739, Spring 2007

MATH 739: Topics in Algebra: Combinatorics of symmetric and quasisymmetric functions (Spring 2007)

Instructor: Louis Billera

Meeting Time & Room

We will study the combinatorial properties of the rings of symmetric and quasisymmetric functions, beginning with the treatment found in Chapter 7 of Stanley's "Enumerative Combinatorics, vol.2". From there we will consider the use of quasisymmetric functions in the enumeration theory of graded and Eulerian partially ordered sets. In particular, we will consider P-partitions and enriched P-partitions, as well as the relationship of the latter to enumeration in polytopes and spherical complexes. As time and interest allows, we can discuss the theory of combinatorial Hopf algebras, due originally to Aguiar, or the application of Eulerian enumeration to the study of Kazhdan-Lusztig polynomials of Bruhat intervals in Coxeter groups.

Prerequisites: Math 631 or Math 434. Knowledge of basic poset theory would be helpful, but not essential.