Quasi-configurations: Building blocks for point-line configurations

Jürgen Bokowski, Vincent Pilaud

Abstract


We study point-line incidence structures and their properties in the projective plane. Our motivation is the problem of the existence of (n_4) configurations, still open for few remaining values of n. Our approach is based on quasi-configurations: point-line incidence structures where each point is incident to at least 3 lines and each line is incident to at least 3 points. We investigate the existence problem for these quasi-configurations, with a particular attention to 3|4-configurations where each element is 3- or 4-valent. We use these quasi-configurations to construct the first (37_4) and (43_4) configurations. The existence problem of finding (22_4), (23_4), and (26_4) configurations remains open.

Keywords


Projective arrangements, point-line incidence structure, (n_k) configurations.

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DOI: https://doi.org/10.26493/1855-3974.642.bbb

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications