On the Expected Number of k-Sets.
On the Face-Vector of a 5-Valent Convex 3-Polytope
On the face-vectors of trivalent convex polyhedra
On the graph labellings arising from phylogenetics
We study semigroups of labellings associated to a graph. These generalise the Jukes-Cantor model and phylogenetic toric varieties defined in [Buczynska W., Phylogenetic toric varieties on graphs, J. Algebraic Combin., 2012, 35(3), 421–460]. Our main theorem bounds the degree of the generators of the semigroup by g + 1 when the graph has first Betti number g. Also, we provide a series of examples where the bound is sharp.
On the Graver complexity of codimension 2 matrices.
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.