Quasi-topological configurations (Seminar DM)

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Quasi-topological configurations

Arjana Žitnik

Torek, 1. april 2014, od 10-12, Plemljev seminar, Jadranska 19

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

A quasiline arrangement with selected vertices belonging to the configuration can be viewed as a map on a closed surface. Such a map can be used to distinguish between two ``distinct" realizations of a combinatorial configuration as a quasiline arrangement.

Glej tudi/See also

Seminar za diskretno matematiko

Osebna orodja