There are no realizable 15_4- and 16_4-configurations

dc.creatorBokowski, Juergen
dc.creatorSchewe, Lars
dc.date2005-05-11
dc.date2005-05-24
dc.date.accessioned2026-07-07T08:54:40Z
dc.date.available2026-07-07T08:54:40Z
dc.descriptionThere exist a finite number of natural numbers n for which we do not know whether a realizable n_4-configuration does exist. We settle the two smallest unknown cases n=15 and n=16. In these cases realizable n_4-configurations cannot exist even in the more general setting of pseudoline-arrangements. The proof in the case n=15 can be generalized to n_k-configurations. We show that a necessary condition for the existence of a realizable n_k-configuration is that n > k^2+k-5 holds.
dc.description11 pages, 8 figures, added pseudoline realizations by Branko Gr{ü}nbaum
dc.identifierhttps://arxiv.org/abs/math/0505205
dc.identifierhttp://arxiv.org/abs/math/0505205
dc.identifierRev. Roumaine Math. Pures Appl. 50 (2005), no. 5-6, 483--493.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146017
dc.subjectMetric Geometry
dc.subject52C30 (Primary), 05B30 (Secondary)
dc.titleThere are no realizable 15_4- and 16_4-configurations
dc.typetext

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