LECTURE 5
Finite elds
5.1. The nite eld method
In this lecture we will describe a method based on nite elds for computing the
characteristic polynomial of an arrangement dened over Q. We will then discuss
several interesting examples. The main result (The
LECTURE 4
Broken circuits, modular elements, and supersolvability
This lecture is concerned primarily with matroids and geometric lattices. Since
the intersection lattice of a central arrangement is a geometric lattice, all our results
can be applied to a
LECTURE 3
Matroids and geometric lattices
3.1. Matroids
A matroid is an abstraction of a set of vectors in a vector space (for us, the normals
to the hyperplanes in an arrangement). Many basic facts about arrangements
(especially linear arrangements) and
LECTURE 2
Properties of the intersection poset and graphical
arrangements
2.1. Properties of the intersection p oset
Let A be an arrangement in the vector space V . A subarrangement of A is a
subset B A. Thus B is also an arrangement in V . If x L(A), den
2
R. STANLEY, HYPERPLANE ARRANGEMENTS
LECTURE 1
Basic denitions, the intersection poset and the
characteristic polynomial
1.1. Basic denitions
The following notation is used throughout for certain sets of numbers:
N
P
Z
Q
R
R+
C
[m]
nonnegative integers
p