LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies
| Autor: | Habert, Luc, Pocchiola, Michel |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Discrete Comput. Geom., 50 (3): 552-648, 2013 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00454-013-9532-y |
| Popis: | 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 \c{hi} 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 \c{hi} 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. Comment: 100 pages, 73 figures; accepted manuscript version |
| Databáze: | arXiv |
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