Tomaž Pisanski: Seminar za diskretno matematiko 1.12.2009

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Usual and unusual polycyclic configurations

A combinatorial configuration that admits an automorphism g such that all point- and line-orbits have the same size is called a polycyclic configuration. The existence of polycyclic configurations is related to the polycirculant conjecture. A geometric configuration of points and lines is polycyclic if, in addition, g acts as a rotational symmetry in the plane. An introduction to the theory of polycyclic configurations is presented. The role of covering graphs and reduced Levi graphs is emphasized. Several notable examples of polycyclic configurations, such as astral, celestial, movable and floral configurations are considered.

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