Abstract
Consider a labeled convex n-gon in the plane and a point x in general position in the interior. We associate with this a collection ℱ(x) of 3-element sets, namely those 3-element subsets of the vertices which contain x in their interior. We investigate the problem of characterizing those collections of subsets which can be represented in this matter. We give a complete characterization of this and a related problem.
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Edelman, P. H. and Jamison, R. E., ‘The theory of convex geometries’, Geom. Dedicata 19 (1985), 247–270.
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School of Mathematics, University of Minnesota, Minneapolis, MN 55455. This work was supported in part by NSF grant DMS-8700995.
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England. Work done while Hill Visiting Professor at the University of Minnesota.
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Edelman, P.H., Larman, D.G. On characterizing collections arising from N-gons in the plane. Geom Dedicata 33, 83–89 (1990). https://doi.org/10.1007/BF00147603
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DOI: https://doi.org/10.1007/BF00147603