Pattern Recognition on Oriented Matroids

Arbitrary Rank

In this section we show, without explicit using Remark 1.7, that a simple oriented matroid of arbitrary rank has a tope committee. We again use the technique of consecutive reorientations of an initial acyclic oriented matroid 0 on one-element subsets of its ground set.

In order to simplify the exposition, we will define the ith reorientation of 0 to be the oriented matroid −[i]0.

Lemma 1.13. Let 0 := (Et, 0) = (Et, 0) be a simple acyclic ...