Lexicographic Extensions preserve Euclideaness

TL;DR

This paper proves that extending a Euclidean oriented matroid lexicographically preserves its Euclidean property, ensuring the extension maintains the original structure's geometric consistency.

Contribution

It establishes that lexicographic extensions of Euclidean oriented matroids do not violate Euclidean properties, a previously unconfirmed preservation.

Findings

Lexicographic extensions preserve Euclideaness.

Euclidean oriented matroids are stable under lexicographic extension.

Theoretical proof confirming the preservation property.

Abstract

We prove that a lexicographical extension of a Euclidean oriented matroid remains Euclidean.