Constructing Highly Incident Configurations |
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Authors: | Leah Wrenn Berman |
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Institution: | 1.Department of Mathematics & Statistics,University of Alaska Fairbanks,Fairbanks,USA |
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Abstract: | A geometric (q,k)-configuration is a collection of points and straight lines in the Euclidean plane in which each point lies on q lines and each line passes through k points. We say a (q,k)-configuration is highly incident when one (or both) of q or k is strictly greater than 4. In this paper, two simple lemmas are used to construct infinite classes of (2q,2k)-configurations for any q,k≥2; the resulting configurations have non-trivial dihedral symmetry. In particular, this construction produces the only known
infinite class of symmetric 6-configurations. |
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