The University of Michigan Combinatorics Seminar
In this talk we will introduce the concept of irreducible circuits. In a (real) vector arrangement A, these are pairs (v,I) such that I is an independent subset of A, v is a vector in A in the positive linear span of I, and no proper subset of I has any member of A-I in its positive linear span. It is not hard to show that the irreducible circuits of any centrally symmetric vector arrangement determine the associated oriented matroid, and in many cases of interest, in a more efficient and useful way. The latter point will be illustrated by the classification of irreducible circuits in root systems.