Spring 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.

This is a list of topics proposed at the organizational meeting on January 21.

- Discrete Morse theory
- Polytopes
- Oriented matroids
- Design theory and error-correcting codes
- Integer partitions
- Lattice point enumeration
- Lie algebras and representation theory

- T. Chow, "You could have invented spectral sequences," Notices Amer. Math. Soc. 53 (2006), no. 1, 15--19.
- J. Herzog, T. Hibi and N. V. Trung, "Standard graded vertex cover algebras, cycles and leaves," Trans. Amer. Math. Soc. 360 (2008), no. 12, 6231--6249.
- W. Kook, V. Reiner and D. Stanton, "Combinatorial Laplacians of matroid complexes," J. Amer. Math. Soc. 13 (2000), no. 1, 129--148.
- J. Stembridge, "Coxeter cones and their $h$-vectors," Adv. Math. 217 (2008), no. 5, 1935--1961.

**Wednesday 1/21**

Organizational meeting**Wednesday 1/28**

Jeremy Martin

*Counting cubical spanning trees***Wednesday 2/4**

No seminar**Wednesday 2/11**

Jeremy Martin

*Counting cubical spanning trees II***Wednesday 2/18**

Marge Bayer

*Polytopes***Wednesday 2/25**

Jay Schweig and Jeremy Martin

Discussion of Kook, Reiner and Stanton, "Combinatorial Laplacians of matroid complexes", J. Amer. Math. Soc. 13 (2000), no. 1, 129--148.**Wednesday 3/4**

Tom Enkosky

Discussion of Herzog, Hibi, Trung, and Zheng, "Standard graded vertex cover algebras, cycles and leaves", Trans. Amer. Math. Soc. 360 (2008), no. 12, 6231--6249**Wednesday 3/11**

Jana Goodman (Emporia State University)

Discussion of K.Q. Ji, "A Combinatorial Proof of Andrews' Smallest Parts Partition Function ", Electronic J. Comb. 15 (2008), article #N12.**Wednesday 3/18**

No seminar - Spring Break**Wednesday 3/25**

Brandon Humpert

*Combinatorial Games and Surreal Numbers***Wednesday 4/1**

Brandon Humpert

*Combinatorial Games and Surreal Numbers, II***Wednesday 4/8**

No seminar**Wednesday 4/15**

No seminar**Wednesday 4/22**

Fred Galvin

*Cliques*__Abstract:__Some dull results and interesting problems inspired by the (easy) question: what is the minimum number of (maximal) cliques in an n-vertex graph and its complement? The answer to that question is n + 1; the minimizing graphs were characterized in my first paper on graph theory, a joint work with M. M. Krieger. We get nontrivial questions by changing "graph" to "hypergraph", or by changing "an n-vertex graph and its complement" to "an edge decomposition of the complete graph on n vertices into k spanning subgraphs". Some partial results on these questions are obtained in my posthumous paper with P. Erdos and M. M. Krieger.**Wednesday 4/29**

Jeremy Martin

*Pseudo-Cell Posets*__Abstract:__Jay Schweig and I are currently wondering when the edges of a ranked poset can be labeled with integers so as to mimic the degrees of the attaching maps in a cell complex - and if so, if one can say anything intelligent about the resulting Laplacian eigenvalues. I will explain all this, likely very informally.**Wednesday 5/6**

TBA

Jeremy Martin's home page

Last updated Tue 4/29/09