Geodesic
Quasi-configurations: Building blocks for point-line configurations
Ars Mathematica Contemporanea, Tome 10 (2016) no. 1, pp. 99-112.

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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.
DOI : 10.26493/1855-3974.642.bbb
Keywords: Projective arrangements, point-line incidence structure, (n_k) configurations. 
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Jürgen Bokowski; Vincent Pilaud. Quasi-configurations: Building blocks for point-line configurations. Ars Mathematica Contemporanea, Tome 10 (2016) no. 1, pp. 99-112. doi : 10.26493/1855-3974.642.bbb. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.642.bbb/

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