Fall 2009

The KU Combinatorics Seminar meets on **Wednesdays,
3:00--4:00 PM in Snow 408.**

Please contact Jeremy Martin if you are interested in speaking.

**Wednesday 8/26**

Jay Schweig

*The h-Vector of a Lattice Path Matroid*__Abstract:__Much of matroid theory is somehow connected to the following question: Given a sequence (f_0, f_1, ..., f_r) of positive integers, when does there exist a matroid M such that each f_i is the number of independent sets of M. Stanley has conjectured a property of such sequences, which we prove in the special case when M is a lattice path matroid. We also prove an interesting connection between our result and the class of discrete polymatroids, and discuss some potential problems in extending the results. No knowledge of matroid theory will be assumed, although it may help to know the basic definitions beforehand.**Wednesday 9/2**

No seminar**Wednesday 9/9**

Kyungyong Lee (Purdue University)

*q,t-Catalan numbers*__Abstract:__The q,t-Catalan numbers naturally occur in the study of Macdonald polynomials, which are an important family of multivariable orthogonal polynomials introduced by Macdonald in 1988 with applications to a wide variety of subjects including Hilbert schemes, harmonic analysis, representation theory, mathematical physics, and algebraic combinatorics. Haiman and Garsia-Haglund proved that they are polynomials of q and t with positive coefficients.

Finding coefficients of the n-th q,t-Catalan number is equivalent to counting how many Catalan paths in the n*n square have the same statistics. We give simple upper bounds on coefficients in terms of partition numbers, and describe all coefficients which achieve the upper bounds.**Wednesday 9/16**

No seminar**Wednesday 9/23**

Jeremy Martin

*The Billera-Jia-Reiner invariant*

(Relevant article: "A quasisymmetric function for matroids" by L. Billera, N. Jia and V. Reiner)**Wednesday 9/30**

Jeremy Martin

*Combinatorial Hopf algebras*

**Wednesday 10/7**

TBA**Wednesday 10/14**

No seminar (Fall Break)**Wednesday 10/21**

No seminar (everyone will be out of town)**Wednesday 10/28**

No seminar**Wednesday 11/4**

Jeremy Martin

*Random Spanning Trees***Wednesday 11/11**

Brandon Humpert

*Combinatorial Hopf Algebras*

(Relevant article: "Combinatorial Hopf algebras and generalized Dehn-Sommerville relations" by M. Aguiar, N. Bergeron and F. Sottile)**Wednesday 11/18**

No seminar. Please attend the Analysis Seminar talk "k-point Configurations in Vector Spaces over Finite Fields" (by Jeremy Chapman, U. of Missouri) at 3:00 PM in Snow 306.**Wednesday 11/25**

No seminar - Thanksgiving**Wednesday 12/2**

Tom Enkosky

*Drawings of Graphs in Arbitrary Dimensional Space***(Ph.D. Oral Comprehensive Exam)****Wednesday 12/9**

Brandon Humpert

*Combinatorial Hopf Algebras II*

Jeremy Martin's home page

Last updated Tue 11/17/09