We prove some preliminary results concerning two questions of O.Karpenkov: (1) What is the number of decompositions of torus of dimension 2 into given number f of regions by unions of n geodesics? (2) On the plane there are n circles not in general position, every pair of cicles has at least one common point. What is the set of all possible numbers of regions?
Symmetry of $f$-vectors of toric arrangements in general position and some applications
On sets of $n$ points in general position that determine lines that can be pierced by $n$ points
On the connectivity of the disjointness graph of segments of point sets in general position in the plane
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