English

Vertex-shellings of Euclidean Oriented Matroids

Combinatorics 2025-01-22 v2

Abstract

A Euclidean oriented matroid program yields a partial ordering of the cocircuits of its cocircuit graph. We show that every linear extension of that ordering yields a topological sweep and induces a recursive atom-ordering (a shelling of the cocircuits) of the tope cell of the feasible region. We extend that sweep and obtain also a vertex-shelling of the whole oriented matroid and finally describe some connections to the notion of stackable zontopal tilings and to a counterexample of a conjecture of A. Mandel.

Keywords

Cite

@article{arxiv.2306.07184,
  title  = {Vertex-shellings of Euclidean Oriented Matroids},
  author = {Winfried Hochstättler and Michael Wilhelmi},
  journal= {arXiv preprint arXiv:2306.07184},
  year   = {2025}
}

Comments

21 pages, 1 figures, the article is splitted into two smaller articles, this one and a companion article, which is called 'Lexicographic extensions preserve Euclideaness'

R2 v1 2026-06-28T11:03:03.569Z