Quasi-configurations: building blocks for point-line configurations

@article{Bokowski2016QuasiconfigurationsBB,
  title={Quasi-configurations: building blocks for point-line configurations},
  author={J{\"u}rgen Bokowski and Vincent Pilaud},
  journal={Ars Math. Contemp.},
  year={2016},
  volume={10},
  pages={99-112}
}
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… 

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