DCG
2000
13 years 4 months ago
2000
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...
DCG
2000
13 years 4 months ago
2000
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...
DCG
2000
13 years 4 months ago
2000
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...
DCG
2000
13 years 4 months ago
2000
DCG
2000
13 years 4 months ago
2000
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 ...
DCG
2000
13 years 4 months ago
2000
DCG
2000
13 years 4 months ago
2000
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,...
DCG
2000
13 years 4 months ago
2000
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...
DCG
2000
13 years 4 months ago
2000
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...
DCG
2000
13 years 4 months ago
2000
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...