منابع مشابه
On the Cocircuit Graph of an Oriented Matroid
In this paper we consider the cocircuit graph G M of an oriented matroid M, the 1-skeleton of the cell complex W formed by the span of the cocircuits of M. In general, W is not determined by G M. However, we show that if the vertex set resp. edge set] of G M is properly labeled by the hyperplanes resp. colines] of M, G M determines W. Also we prove that, when M is uniform, the cocicuit graph to...
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In this paper we consider the cocircuit graph GM of an oriented matroidM, the 1-skeleton of the cell complexW formed by the span of the cocircuits ofM. In general,W is not determined by GM. However, we show that if the vertex set (resp. edge set) of GM is properly labeled by the hyperplanes (resp. colines) ofM, GM determinesW . Also we prove that, whenM is uniform, the cocircuit graph together ...
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Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and new results about line-closed geometries. We complement these topics by showing that line-closure gives simple geometric proofs of the (mostly known) basic results about Dowling lattices. We pursue the topic of line-clo...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2000
ISSN: 0179-5376
DOI: 10.1007/s004540010031