On representing contexts in line arrangements |
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Authors: | Jürgen Bokowski Wolfgang Kollewe |
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Affiliation: | (1) Mathematics Department, University of Darmstadt, Schlossgartenstrasse, 7, 6100 Darmstadt, Germany |
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Abstract: | Acontext is defined to be a triple (G, M, J) of setsG, M and an incidence relationJ G×M.A finite set ofn oriented lines in general position in the euclidean plane induces a cell decomposition of the plane. For a givenk-element subset of cells of dimension 2, we define an incidence relationJ × as follows:ti andlj are incident if and only ifti lies on the positive side with respect tolj.We call a context (G, M, J)represented in a line arrangement if and only if there are relation preserving bijections betweenG and ,M and , respectively. We study conditions for a context to be representable in a line arrangement.Especially, we provide a non-trivial infinite class of contexts which can not be represented in a line arrangement. |
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Keywords: | Primary 05B35 secondary 52Bxx |
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