1-bend 3-D orthogonal box-drawings: Two open problems solved.
A Bound on Local Minima of Arrangements that Implies the Upper Bound Theorem.
A Characterisation of a Simplex.
A combinatorial proof of a formula for Betti numbers of a stacked polytope.
A construction for periodically-cyclic Gale -polytopes.
A Decomposition of 2-Weak Vertex-Packing Polytopes.
A Generalization of Dehn-Sommerville Relations to Simple Stratified Spaces.
A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces
A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex...
A New Necessary Condition for the Vertex Visibility Graphs of Simple Polygons.
A point in many triangles.
A simpler construction of volume polynomials for a polyhedron.
A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria
Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending...
Algebraic shifting and sequentially Cohen-Macaulay simplicial complexes.
Algorithms for Triangulating Polyhedra Into a Small Number of Tethraedra
An inequality concerning edges of minor weight in convex 3-polytopes
Let be the number of edges in a convex 3-polytope joining the vertices of degree i with the vertices of degree j. We prove that for every convex 3-polytope there is ; moreover, each coefficient is the best possible. This result brings a final answer to the conjecture raised by B. Grünbaum in 1973.
Automorphismen von polyedrischen Graphen.
Bemerkungen zu Determinanten-Theorie. Auszug aus Briefen an Herrn Baltzer.
Bergman complexes, Coxeter arrangements, and graph associahedra.
Bose's vertex theorem for simply closed polygons.
Cardinality estimates for piecewise congruences of convex polygons.