The action of the symmetric group on a generalized partition semilattice.
The active bijection between regions and simplices in supersolvable arrangements of hyperplanes.
The cd-index of Bruhat intervals.
The concept of cutting vectors for vector systems in the Euclidean plane.
The integral cohomology algebras of ordered configuration spaces of spheres.
The lattices and Möbius functions of stable closed subrootsystems and Hyperplane complements for classical Weyl Groups.
The Salvetti complex and the little cubes
For a real central arrangement , Salvetti introduced a construction of a finite complex Sal which is homotopy equivalent to the complement of the complexified arrangement in [Sal87]. For the braid arrangement , the Salvetti complex Sal serves as a good combinatorial model for the homotopy type of the configuration space of points in , which is homotopy equivalent to the space of k little -cubes. Motivated by the importance of little cubes in homotopy theory, especially in the study of...
The upper bound conjecture for arrangements of halfspaces.
The upper bound conjecture for arrangements of half-spaces.
The vanishing of the cohomology of the Orlik-Solomon algebras.
Topological criteria for -formal arrangements.
Topological Order Complexes and Resolutions of Discriminant Sets
Topological order complexes and resolutions of discriminant sets.
Topology of arrangements and position of singularities
This work contains an extended version of a course given in Arrangements in Pyrénées. School on hyperplane arrangements and related topics held at Pau (France) in June 2012. In the first part, we recall the computation of the fundamental group of the complement of a line arrangement. In the second part, we deal with characteristic varieties of line arrangements focusing on two aspects: the relationship with the position of the singular points (relative to projective curves of some prescribed degrees)...
Two Constructions of Oriented Matroids with Disconnected Extension Space.
Two interesting oriented matroids.
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Vapnik-Chervonenkis Dimension and (Pseudo-)Hyperplane Arrangements.
Weighted complete intersections and lattice points.
"What Is a Complex Matroid?"