Article Dans Une Revue Ars Mathematica Contemporanea Année : 2016

Quasi-configurations: building blocks for point-line configurations

Résumé

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.

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hal-01276812 , version 1 (20-02-2016)

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  • HAL Id : hal-01276812 , version 1

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Jürgen Bokowski, Vincent Pilaud. Quasi-configurations: building blocks for point-line configurations. Ars Mathematica Contemporanea, 2016, 10 (1), pp.99-112. ⟨hal-01276812⟩
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