The Disk-Packing Constant
The Ehrhart polynomial of a lattice -simplex.
The impossibility of a tesselation of the plane into equilateral triangles whose sidelengths are mutually different, one of them being minimal.
The integral cohomology algebras of ordered configuration spaces of spheres.
The lattice polytope problem.
The lattices and Möbius functions of stable closed subrootsystems and Hyperplane complements for classical Weyl Groups.
The local theorem for monotypic tilings.
The lonely vertex problem.
The Maximum Number of Second Smallest Distances in Finite Planar Sets.
The maximum number of unit distances among points in dimension four.
The maximum of the smallest maximal coordinate of the minimum vectors in 6-lattices equals 1.
The Maximum Size of a Convex Polygon in a Restricted Set of Points in the Plane.
The multiplicity of partial coverings of space
The Number of Different Distances Determined by a Set of Points in the Euclidean Plane.
The optimal ball and horoball packings of the Coxeter tilings in the hyperbolic 3-space.
The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic -space.
The possibility of extending factorization results to infinite Abelian groups.
The projective interpretation of the eight 3-dimensional homogeneous geometries.
The Rhombidodecahedral Tessellation of 3-Space and a Particular 15-Vertex Triangulation of the 3-Dimensional Torus.
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...