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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Planar point sets with many triple lines (which contain at least threedistinct points of the set) have been studied for 180 years, started withJackson and followed by Sylvester. Green and Tao has shown recently that themaximum possible number of triple lines for an n element set is [n(n - 3)/6] +1. Here we address the related problem of describing the structure of theasymptotically near-optimal configurations, i.e., of those for which the numberof straight lines, which go through three or more points, has a quadratic(i.e., best possible) order of magnitude. We pose the problem whether suchpoint sets must always be related to cubic curves. To support this conjecturewe settle various special cases; some of them are also related to thefour-in-a-line problem of Erd\H{o}s.

On Triple Lines and Cubic Curves --- the Orchard Problem revisited