Pattern Recognition on Oriented Matroids: K*-Vectors and Reorientations

TL;DR

This paper investigates how reorientations of simple oriented matroids influence their K*-vectors, which count specific tope committees, using inclusion-exclusion principles to analyze these effects.

Contribution

It introduces a method to analyze the impact of reorientations on K*-vectors in oriented matroids, providing new insights into their combinatorial structure.

Findings

Reorientations alter K*-vector components systematically.

Inclusion-exclusion effectively determines reorientation effects.

Results enhance understanding of oriented matroid reconfigurations.

Abstract

The components of K*-vectors associated to a simple oriented matroid M are the numbers of general or special tope committees for M. Using the principle of inclusion-exclusion, we determine how the reorientations of M on one-element subsets of its ground set affect K*-vectors.