Highly Incident Configurations with Chiral Symmetry |
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Authors: | Leah Wrenn Berman Jill R Faudree |
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Institution: | 1. Department of Mathematics & Statistics, University of Alaska Fairbanks, Fairbanks, AK, USA
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Abstract: | A geometric $k$ -configuration is a collection of points and straight lines in the plane so that $k$ points lie on each line and $k$ lines pass through this point. We introduce a new construction method for constructing $k$ -configurations with non-trivial dihedral or chiral (i.e., purely rotational) symmetry, for any $k \ge 3$ ; the configurations produced have $2^{k-2}$ symmetry classes of points and lines. The construction method produces the only known infinite class of symmetric geometric 7-configurations, the second known infinite class of symmetric geometric 6-configurations, and the only known 6-configurations with chiral symmetry. |
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