Abstract
Acontext is defined to be a triple (G, M, J) of setsG, M and an incidence relationJ ⊂ G×M.
A finite set ℒ ofn oriented lines in general position in the euclidean plane induces a cell decomposition of the plane. For a givenk-element subset ℐ of cells of dimension 2, we define an incidence relationJ ⊂ ℐ × ℒ as follows:t i andl j are incident if and only ift i lies on the positive side with respect tol j .
We call a context (G, M, J)represented in a line arrangement if and only if there are relation preserving bijections betweenG and ℐ,M and ℒ, 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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Bokowski, J., Kollewe, W. On representing contexts in line arrangements. Order 8, 393–403 (1991). https://doi.org/10.1007/BF00571189
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DOI: https://doi.org/10.1007/BF00571189