13 citations · 18 across the 7 of their papers we have counts for
7 papers
A lower bound on opaque sets
Akitoshi Kawamura, Sonoko Moriyama, Yota Otachi +1
It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This…
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…
Families of polytopal digraphs that do not satisfy the shelling property
David Avis, Hiroyuki Miyata, Sonoko Moriyama
A polytopal digraph is an orientation of the skeleton of a convex polytope . The possible non-degenerate pivot operations of the simplex method in solving a linear progra…
On the Existence of Hamiltonian Paths for History Based Pivot Rules on Acyclic Unique Sink Orientations of Hypercubes
Yoshikazu Aoshima, David Avis, Theresa Deering +2
An acyclic USO on a hypercube is formed by directing its edges in such as way that the digraph is acyclic and each face of the hypercube has a unique sink and a unique source. A pa…
From Bell Inequalities to Tsirelson's Theorem: A Survey
David Avis, Sonoko Moriyama, Masaki Owari
The first part of this paper contains an introduction to Bell inequalities and Tsirelson's theorem for the non-specialist. The next part gives an explicit optimum construction for…
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 $…