46 citations · 100 across the 13 of their papers we have counts for
5 papers · 1 filter
Complete enumeration of small realizable oriented matroids
Komei Fukuda, Hiroyuki Miyata, Sonoko Moriyama
Enumeration of all combinatorial types of point configurations and polytopes is a fundamental problem in combinatorial geometry. Although many studies have been done, most of them…
A linear equation for Minkowski sums of polytopes relatively in general position
Komei Fukuda, Christophe Weibel
The objective of this paper is to study a special family of Minkowski sums, that is of polytopes relatively in general position. We show that the maximum number of faces in the sum…
The Holt-Klee condition for oriented matroids
Komei Fukuda, Sonoko Moriyama, Yoshio Okamoto
Holt and Klee have recently shown that every (generic) LP orientation of the graph of a -polytope satisfies a directed version of the -connectivity property, i.e. there are $…
Every non-Euclidean oriented matroid admits a biquadratic final polynomial
Komei Fukuda, Sonoko Moriyama, Hiroki Nakayama
Richter-Gebert proved that every non-Euclidean uniform oriented matroid admits a biquadratic final polynomial. We extend this result to the non-uniform case.
On f-vectors of Minkowski additions of convex polytopes
Komei Fukuda, Christophe Weibel
The objective of this paper is to present two types of results on Minkowski sums of convex polytopes. The first is about a special class of polytopes we call perfectly centered and…