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arXiv · 1101.1022

LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies

Luc Habert·Michel Pocchiola
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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 \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.

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Luc Habert, Michel Pocchiola. 2014-10-05. LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies. https://doi.org/10.1007/s00454-013-9532-y

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