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LR Characterization of Chirotopes of Finite Planar Families of Pairwise Disjoint Convex bodies
| Content Provider | Paperity |
|---|---|
| Author | Habert, Luc Pocchiola, Michel |
| Abstract | We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint convex bodies: a map \(\chi \) on the set of 3-subsets of a finite set \(I\) is a chirotope of finite planar families of pairwise disjoint convex bodies if and only if for every 3-, 4-, and 5-subset \(J\) of \(I\) the restriction of \(\chi \) to the set of 3-subsets of \(J\) is a chirotope of finite planar families of pairwise disjoint convex bodies. Our main tool is the polarity map, i.e., the map that assigns to a convex body the set of lines missing its interior, from which we derive the key notion of arrangements of double pseudolines, introduced for the first time in this paper. |
| Starting Page | 552 |
| Ending Page | 648 |
| File Format | HTM / HTML |
| ISSN | 01795376 |
| DOI | 10.1007/s00454-013-9532-y |
| Issue Number | 3 |
| Journal | Discrete & Computational Geometry |
| Volume Number | 50 |
| e-ISSN | 14320444 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2013-08-27 |
| Access Restriction | Open |
| Subject Keyword | Discrete geometry Pseudoline arrangements Chirotopes Convexity Projective planes |
| Content Type | Text |
| Resource Type | Article |
| Subject | Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology |
