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DCG
2000
94views more  DCG 2000»
13 years 11 months ago
Finding Small Triangulations of Polytope Boundaries Is Hard
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...
Jürgen Richter-Gebert
DCG
2000
44views more  DCG 2000»
13 years 11 months ago
Icosahedra Constructed from Congruent Triangles
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...
E. N. Miller
DCG
2000
84views more  DCG 2000»
13 years 11 months ago
Convex and Linear Orientations of Polytopal Graphs
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...
J. Mihalisin, Victor Klee
DCG
2000
59views more  DCG 2000»
13 years 11 months ago
Decomposing the Secondary Cayley Polytope
T. Michiels, Ronald Cools
DCG
2000
79views more  DCG 2000»
13 years 11 months ago
Mutation Polynomials and Oriented Matroids
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 ...
J. Lawrence
DCG
2000
53views more  DCG 2000»
13 years 11 months ago
Integer Optimization on Convex Semialgebraic Sets
Leonid Khachiyan, Lorant Porkolab
DCG
2000
67views more  DCG 2000»
13 years 11 months ago
A Theorem on Higher Bruhat Orders
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,...
Stefan Felsner, Helmut Weil
DCG
2000
75views more  DCG 2000»
13 years 11 months ago
Cutting Polytopes and Flag f-Vectors
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...
DCG
2000
90views more  DCG 2000»
13 years 11 months ago
On the Cocircuit Graph of an Oriented Matroid
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...
Raul Cordovil, Komei Fukuda, António Guedes...
DCG
2000
45views more  DCG 2000»
13 years 11 months ago
Relations in SO (3) Supported by Geodetic Angles
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...
John H. Conway, Charles Radin, L. Sadun