Pattern Recognition on Oriented Matroids

9Halfspaces, Convex Sets, and Tope Committees

In this chapter, for enumerating tope committees, we apply the Principle of Inclusion–Exclusion to subsets of maximal covectors contained in the halfspaces of a simple oriented matroid, and to convex subsets of its ground set.

Let = (Et, ) be a simple oriented matroid which is not acyclic. Recall that the family $K_k^{*}\left(M\right)$ of tope committees of size k, 3 ≤ k ≤ ||–3, for is defined to be the collection ...