Euclidean intersection properties
type: Item
instance of: scholarly article
title: Euclidean intersection properties
zbMATH Open document ID: 0619.05016
DOI: 10.1016/0095-8956(89)90061-0
author: Achim Bachem
author: Alfred Wanka
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: There are matroids which have Euclidean and non-Euclidean orientations and there are also matroids whose inherent structure does not allow any Euclidean orientation. In this paper we discuss some lattice theoretic properties of matroids which when used in an oriented version guarantee Euclideanness. These properties depend all on the existence of intersections of certain flats (which is equivalent to Euclideanness interpreted in the Las Vergnas notation of oriented matroids). We introduce three classes of matroids having various intersection properties and show that two of them cannot be characterized by excluding finitely many minors.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4004201
zbMATH Keywords: Euclidean orientations
zbMATH Keywords: intersection properties
zbMATH Keywords: lattices
zbMATH Keywords: oriented matroids
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90061-0
OpenAlex ID: W2069914940
cites work: On sticky matroids
cites work: Separation theorems for oriented matroids
cites work: Adjoints of a Geometry
cites work: Oriented Matroids of Rank Three and Arrangements of Pseudolines
cites work: Q5619114
cites work: Convexity in oriented matroids
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description: scientific article; zbMATH DE number 4004201