Enumerating topological $(n_k)$-configurations
Résumé
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.
Fichier principal
BokowskiPilaud_TopologicalConfigurations_CGTA.pdf (791.64 Ko)
Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...