A combinatorial perspective on the non-Radon partitions
type: Item
instance of: scholarly article
title: A combinatorial perspective on the non-Radon partitions
zbMATH Open document ID: 0571.05014
DOI: 10.1016/0097-3165(85)90019-6
author: Raul Cordovil
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: If (M(E),0) is an oriented matroid without loops defined on a finite set of points E in \({\mathbb{R}}^ d\), then it is uniquely determined by the subsets \(A\subseteq E\) for which there exists a hyperplane strictly separating A from E-A. The author considers the poset of these A's and computes its Möbius function and in a special case its homotopy type. This generalizes results of \textit{P. H. Edelman} on a partial order on regions formed by hyperplanes [Trans. Am. Math. Soc. 283, 617-631 (1984; Zbl 0555.06003)].
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 3910410
zbMATH Keywords: oriented matroid
zbMATH Keywords: poset
zbMATH Keywords: Möbius function
reviewed by: David M. Bressoud
MaRDI profile type: Publication
full work available at URL: 0097-3165(85)90019-6
OpenAlex ID: W1972166787
cites work: Homotopy type of posets and lattice complementation
cites work: Orientability of matroids
cites work: A combinatorial perspective on the Radon convexity theorem
cites work: Sur les matroides orientes de rang 3 et les arrangements de pseudodroites dans le plan projectif réel
cites work: Euler's relation, Moebius functions and matroid identities
cites work: A problem of McMullen on the projective equivalences of polytopes
cites work: Q5556250
cites work: A Partial Order on the Regions of R n Dissected by Hyperplanes
cites work: Oriented matroids
cites work: On the Interpretation of Whitney Numbers Through Arrangements of Hyperplanes, Zonotopes, Non-Radon Partitions, and Orientations of Graphs
cites work: Q5547252
cites work: Convexity in oriented matroids
cites work: Q4189292
cites work: On the realization of convex polytopes, Euler's formula and Möbius functions
cites work: Q5638112
cites work: Q4053713
cites work: Facing up to arrangements: face-count formulas for partitions of space by hyperplanes
description: scientific article; zbMATH DE number 3910410