On the monotone upper bound problem.
On the monotonicity of the volume of hyperbolic convex polyhedra.
On the notion of the combinatorial -parametric property for polyhedra.
On the Number of Convex Lattice Polytopes.
On the Number of Critical Free Contacts of a Convex Polygonal Object Moving in Two-Dimensional Polygonal Space.
On the number of facets of three-dimensional Dirichlet stereohedra. II: Non-cubic groups.
On the Number of Minimal 1-Steiner Trees.
On the Number of Views of Polyhedral Terrains.
On the Realization of Convex Polytopes, Euler's Formula and Möbius Functions (Short Communication)
On the Realization of Convex Polytopes, Euler's Formula and Möbius Functions
On the refinements of a polyhedral subdivision.
Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced subdivision....
On the separation of parametric convex polyhedral sets with application in MOLP
We investigate diverse separation properties of two convex polyhedral sets for the case when there are parameters in one row of the constraint matrix. In particular, we deal with the existence, description and stability properties of the separating hyperplanes of such convex polyhedral sets. We present several examples carried out on PC. We are also interested in supporting separation (separating hyperplanes support both the convex polyhedral sets at given faces) and permanent separation (a hyperplane...
On the Stanley Ring of a Cubical Complex.
On the structure of the quadratic Boolean problem polytope
On the volume of a certain polytope.
On the volume of the polytope of doubly stochastic matrices.
On the volume of unbounded polyhedra in the hyperbolic space.
On the volumes of hyperbolic 5-orthoschemes and the Trilogarithm.
On the Weight of Minor Faces in Triangle-Free 3-Polytopes
The weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or a 5-face with w ≤ 17. Here, the bound 17 is sharp, but it was still unknown whether 21 is sharp. The purpose of this paper is to improve this 21 to 20, which is best possible.
On the Zone of a Surface in a Hyperplane Arrangement.