We prove that it is NP-hard to decide whether a polyhedral 3-ball can be triangulated with k simplices. The construction also implies that it is difficult to find the minimal trian...
It is possible to construct a figure in 3 dimensions which is combinatorially equivalent to a regular icosahedron, and whose faces are all congruent but not equilateral. Such icos...
This paper examines directed graphs related to convex polytopes. For each fixed d-polytope and any acyclic orientation of its graph, we prove there exist both convex and concave fu...
Several polynomials are of use in various enumeration problems concerning objects in oriented matroids. Chief among these is the Radon catalog. We continue to study these, as well ...
We show that inclusion order and single-step inclusion coincide for higher Bruhat orders B(n; 2), i.e., B(n; 2) = B (n; 2). Mathematics Subject Classi cations (1991). 06A06, 51G05,...
We show how the flag f -vector of a polytope changes when cutting off any face, generalizing work of Lee for simple polytopes. The result is in terms of explicit linear operators o...
Richard Ehrenborg, D. Johnston, R. Rajagopalan, Ma...
In this paper we consider the cocircuit graph GM of an oriented matroid M, the 1-skeleton of the cell complex W formed by the span of the cocircuits of M. In general, W is not dete...
We consider rotations A, B of finite order in SO(3), about axes separated by an angle of restricted type, and attempt to classify the possible group relations between A and B. We s...