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Some Combinatorial Properties of Finite Line-Systems in the Euclidean Plane

Some Combinatorial Properties of Finite Line-Systems in the Euclidean Plane We consider finite systems of straight lines in the Euclidean plane 𝐑 2 with some of their combinatorial characteristics. Euler's formula is applied for obtaining results of combinatorial type for such systems. In particular, a lower estimate for the number of two-sided and three-sided domains determined by a given finite line-system in 𝐑 2 is presented and it is shown that this estimate is precise in a certain sense. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Some Combinatorial Properties of Finite Line-Systems in the Euclidean Plane

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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2007.681
Publisher site
See Article on Publisher Site

Abstract

We consider finite systems of straight lines in the Euclidean plane 𝐑 2 with some of their combinatorial characteristics. Euler's formula is applied for obtaining results of combinatorial type for such systems. In particular, a lower estimate for the number of two-sided and three-sided domains determined by a given finite line-system in 𝐑 2 is presented and it is shown that this estimate is precise in a certain sense.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Dec 1, 2007

Keywords: Euclidean plane; line-system; point-system; convex hull; Euler's formula

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