Lower-Bound Theorems for Pseudomanifolds.
Minimal fixing systems for convex bodies.
Mixture decompositions of exponential families using a decomposition of their sample spaces
We study the problem of finding the smallest such that every element of an exponential family can be written as a mixture of elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of the corresponding convex support polytopes and results from coding theory. We show that is the smallest number for which any distribution of
Nonoverlap of the Star Unfolding.
Note on Petri and Hamiltonian cycles in cubic polyhedral graphs.
Note on Petrie and Hamiltonian cycles in cubic polyhedral graphs
In this note we show that deciding the existence of a Hamiltonian cycle in a cubic plane graph is equivalent to the problem of the existence of an associated cubic plane multi-3-gonal graph with a Hamiltonian cycle which takes alternately left and right edges at each successive vertex, i.ei̇t is also a Petrie cycle. The Petrie Hamiltonian cycle in an -vertex plane cubic graph can be recognized by an -algorithm.
On a dynamics in rational polygonal billiards
On braxtopes, a class of generalized simplices.
On deformations of spherical isometric foldings
The behavior of special classes of isometric foldings of the Riemannian sphere under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding defined by .
On faces of a convex polyhedron in with a small number of sides.
On longest circuits in certain non-regular planar graphs
On rainbowness of semiregular polyhedra
We introduce the rainbowness of a polyhedron as the minimum number such that any colouring of vertices of the polyhedron using at least colours involves a face all vertices of which have different colours. We determine the rainbowness of Platonic solids, prisms, antiprisms and ten Archimedean solids. For the remaining three Archimedean solids this parameter is estimated.
On simple polytopes.
On the convex hull of projective planes
We study the finite projective planes with linear programming models. We give a complete description of the convex hull of the finite projective planes of order 2. We give some integer linear programming models whose solution are, either a finite projective (or affine) plane of order n, or a (n+2)-arc.
On the number of facets of three-dimensional Dirichlet stereohedra. II: Non-cubic groups.
On the Number of Views of Polyhedral Terrains.
On the volume of the polytope of doubly stochastic matrices.
On the Zone of a Surface in a Hyperplane Arrangement.
Projected products of polygons.
Proof of a conjecture of Chan, Robbins, and Yuen.