Pattern Recognition on Oriented Matroids: Halfspaces, Convex Sets and Tope Committees

TL;DR

This paper applies the inclusion-exclusion principle to oriented matroids to efficiently enumerate tope committees by analyzing maximal covectors and convex subsets.

Contribution

It introduces a novel application of inclusion-exclusion to oriented matroids for enumeration of tope committees, linking convex sets and covectors.

Findings

Effective enumeration method for tope committees

Connection between convex sets and covectors in oriented matroids

Enhanced understanding of the structure of tope committees

Abstract

The principle of inclusion-exclusion is applied to subsets of maximal covectors contained in halfspaces of a simple oriented matroid and to convex subsets of its ground set for enumerating tope committees.