A note on the Lawrence-Krammer-Bigelow representation.
A Relation between the Weyl Group W(e8) and Eight-Line Arrangements on a Real Projective Plane
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.The Weyl group W(E8) acts on the con guration space of systems of labelled eight lines on a real projective plane. With a system of eight lines with a certain condition, a diagram consisting of ten roots of the root system of type E8 is associated. We have already shown the existence of a W(E8)-equivariant map of the totality of such diagrams to the set of systems of...
An arrangement of pseudocircles not realizable with circles.
Cubic partial cubes from simplicial arrangements.
Equivalence classes of Latin squares and nets in
The fundamental combinatorial structure of a net in is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in are empty to show some non-existence results for 4-nets in .
On the combinatorial structure of arrangements of oriented pseudocircles.
Some results on odd astral configurations.
Symmetric simplicial pseudoline arrangements.
Unbounded regions in an arrangement of lines in the plane.
Une axiomatisation au premier ordre des arrangements de pseudodroites euclidiennes
Nous définissons une structure logique permettant de représenter les classes d’homéomorphismes des arrangements de pseudodroites du plan euclidien. Nous donnons une axiomatisation finie du premier ordre de la réalisabilité des arrangements de pseudodroites.