Vertex-shellings of Euclidean Oriented Matroids

Abstract

A Euclidean oriented matroid program yields a partial ordering of the cocircuits of its cocircuit graph. We show that every linear extension of that ordering yields a topological sweep and induces a recursive atom-ordering (a shelling of the cocircuits) of the tope cell of the feasible region. We extend that sweep and obtain also a vertex-shelling of the whole oriented matroid and finally describe some connections to the notion of stackable zontopal tilings and to a counterexample of a conjecture of A. Mandel.