Association Schemes

An introduction to association schemes. (Over 200 pages.)

Finite Geometry

Also the table of contents. These notes introduce some topics in finite geometry. This includes the characterization of projective spaces of dimension at least three. (The proof given is group theoretic, and also leads to constructions of translation planes.)

The Colin de Verdiere invariant

Some notes on the Colin de Verdiere invariant. The most useful feature might be a different view point on the strong Arnold (aka Schwarzenegger) condition.

An Introduction to the Möbius function

This is an introduction to the Möbius function of a poset. The chief novelty is in the exposition. We show how order-preserving maps from one poset to another can be used to relate their Möbius functions. We derive the basic results on the Möbius function, applying them in particular to geometric lattices. I once met someone who said that they had found these notes useful. :-)

Symmetries and Eigenvectors

A survey of some of the interactions between graph symmetry and eignevectors.

Tools from Linear Algebra

Chapter 31 of the Wheelbarrow, errr, Handbook of Combinatorics. Expounds on the ways we can use linear algebra in combinatorics.