Computer solution to the 17-point Erd\H{o}s-Szekeres problem

ANZIAM J. 48 (2006), 151-164

Computer solution to the 17-point Erdös-Szekeres problem

George Szekeres
(deceased)
School of Mathematics
University of NSW
Sydney NSW 2052
Australia

and

Lindsay Peters
Pacific Knowledge Systems
Australian Technology Park
Eveleigh NSW 1430
Australia
l.peters@pks.com.au

Abstract

We describe a computer proof of the 17-point version of a conjecture originally made by Klein-Szekeres in 1932 (now commonly known as the "Happy End Problem") that a planar configuration of 17 points, no 3 points collinear, always contains a convex 6-subset. The proof makes use of a combinatorial model of planar configurations, expressed in terms of signature functions satisfying certain simple necessary conditions. The proof is more general than the original conjecture as the signature functions examined represent a larger set of configurations than those which are realisable. Three independent implementations of the computer proof have been developed, establishing that the result is readily reproducible.

Download the article in PDF format (size 104 Kb)

Australian Mathematical Publishing Association Inc.