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1 TU Darmstadt - Technische Universität Darmstadt 2 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau

Abstract : An $n k$-configuration is a set of $n$ points and $n$ lines in the projective plane such that their point-line incidence graph is $k$-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are considered to be straight lines, pseudolines, or just combinatorial lines. We provide an algorithm for generating, for given $n$ and $k$, all topological $n k$-configurations up to combinatorial isomorphism, without enumerating first all combinatorial $n k$-configurations. We apply this algorithm to confirm efficiently a former result on topological $18 4$-configurations, from which we obtain a new geometric $18 4$-configuration. Preliminary results on $19 4$-configurations are also briefly reported.

Keywords : Point-line configuration Pseudoline arrangement Geometric realization Exhaustive enumeration

Author: Jürgen Bokowski - Vincent Pilaud -

Source: https://hal.archives-ouvertes.fr/


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