Name
Abstract | ||
|---|---|---|
LetA be a family ofn pairwise disjoint compact convex sets inRd. Let
<img src="/fulltext-image.asp?format=htmlnonpaginated&src=KR7KH80843513705_html\454_2005_Article_BF02187777_TeX2GIFIE1.gif" border="0" alt="
$$\Phi _d (m) = 2\Sigma _{i = 0}^{d - 1} \left( {_i^{m - 1} } \right)$$
" />. We show that the directed lines inRd, d ≥ 3, can be partitioned into
<img src="/fulltext-image.asp?format=htmlnonpaginated&src=KR7KH80843513705_html\454_2005_Article_BF02187777_TeX2GIFIE2.gif" border="0" alt="
$$\Phi _d \left( {\left( {_2^n } \right)} \right)$$
" /> sets such that any two directed lines in the same set which intersect anyA′⊆A generate the same ordering onA′. The directed lines inR2 can be partitioned into 12n such sets. This bounds the number of geometric permutations onA by 1/2φd ford≥3 and by 6n ford=2. |
Year | DOI | Venue |
|---|---|---|
1990 | 10.1007/BF02187777 | Discrete & Computational Geometry |
Keywords | DocType | Volume |
Planar Graph,Pairwise Disjoint,Discrete Comput Geom,Compact Convex,Convex Polygon | Journal | 5 |
Issue | ISSN | Citations |
1 | 0179-5376 | 25 |
PageRank | References | Authors |
1.98 | 3 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rephael Wenger | 1 | 441 | 43.54 |