Pseudoline arrangements generalize in a natural way arrangements of straight lines,
discarding the straightness aspect, but preserving their basic topological and combinatorial …

The theory of oriented matroids provides a broad setting in which to model, describe, and
analyze combinatorial properties of geometric configurations. Mathematical objects of study …

In a recent paper, Cook et al.(Compos Math 154: 2150–2194, 2018) used the splitting type
of a line arrangement in the projective plane to study the number of conditions imposed by a …

Simplicial arrangements are classical objects in discrete geometry. Their classification
remains an open problem but there is a list conjectured to be complete at least for rank …

We study Milnor fibers of complexified real line arrangements. We give a new algorithm
computing monodromy eigenspaces of the first cohomology. The algorithm is based on the …

We introduce a greedy algorithm optimizing arrangements of lines with respect to a property.
We apply this algorithm to the case of simpliciality: it recovers all known simplicial …

Despite that the study of line arrangements in the projective plane is old and elemental,
there is still a long list of intriguing open questions and applications to modern mathematics …

Since Dumnicki, Szemberg and Tutaj-Gasi\'nska gave in 2013 in [9] the first example of a set
of points in the complex projective plane such that for its homogeneous ideal I the …

We introduce a combinatorial characterization of simpliciality for arrangements of
hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an …

A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971.
These arrangements naturally generalize finite Coxeter arrangements and also the weak …