English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We extend the classical LR characterization of chirotopes of finite planarfamilies of points to chirotopes of finite planar families of pairwise disjointconvex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is achirotope of finite planar families of pairwise disjoint convex bodies if andonly if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to theset of 3-subsets of J is a chirotope of finite planar families of pairwisedisjoint convex bodies. Our main tool is the polarity map, i.e., the map thatassigns to a convex body the set of lines missing its interior, from which wederive the key notion of arrangements of double pseudolines, introduced for thefirst time in this paper.

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