Vertex-shellings of Euclidean Oriented Matroids

Winfried. Hochstättler, Michael Wilhelmi

Publication date: 12 June 2023

Abstract: We prove that a lexicographical extension of a Euclidean oriented matroid remains Euclidean. Based on that result we show that in a Euclidean oriented matroid program there exists a topological sweep inducing 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 zontope tilings and to a counterexample of a conjecture of A. Mandel.

Mathematics Subject Classification ID

Linear programming (90C05) Combinatorial optimization (90C27) Oriented matroids in discrete geometry (52C40)

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