Arjana Žitnik: Combinatorial configurations and quasiline arrangements

Povzetek. It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not  even admit realizations  with pseudoline arrangements, i.e., they are not topological.

We generalize the notion of a pseudoline arrangement to the notion of a quasiline arrangement by relaxing the condition that two pseudolines meet exactly once and show that every combinatorial configuration  can be realized as a quasiline arrangement in the real projective plane. We also generalize well-known tools from pseudoline arrangements such as sweeps or wiring diagrams.