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

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

2005-05-11

arxiv.org/abs/math/0505205v2

Rev. Roumaine Math. Pures Appl. 50 (2005), no. 5-6, 483--493.

Mathematics

Metric Geometry

11 pages, 8 figures, added pseudoline realizations by Branko Gr{\"u}nbaum

Scientific paper

There 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.

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