% File name: booth.tex
\documentclass[a4paper]{article}
\title{Lagrangian Matroids\\ (seminar abstract)}
\author{R. F. Booth}
\date{28th October 1999}
\begin{document}
\maketitle

Classical matroids were introduced in the 1930's by Whitney, and
axiomatise the combinatorial properties of vector configurations in
finite-dimensional vector spaces. A generalisation of the matroid
concept has been introduced by Gelfand and Serganova which associates
matroid-like structures with every Coxeter group, the classical matroid
reappearing as an $A_n$-matroid.

A well-known theorem of Rado associates with every graph a vector
configuration, and thus a classical matroid. Similarly, the main
result of this talk associates each map on an orientable,
2-dimensional surface with a $D_n$-matroid. The proof is cohomological
in nature.

We go on to consider the concept of orientations of vector
configurations and classical matroids, and then to discuss concepts of
orientation of certain (Lagrangian) $B_n$- and $D_n$-matroids.
\end{document}
