ANZIAM  J.  48 (2006), 151-164
Computer solution to the 17-point Erdös-Szekeres problem

George Szekeres
  School of Mathematics
  University of NSW
  Sydney NSW 2052
Lindsay Peters
  Pacific Knowledge Systems
  Australian Technology Park
  Eveleigh NSW 1430

We describe a computer proof of the 17-point version of a conjecture originally made by Klein-Szekeres in 1932 (now commonly known as the "Happy End Problem") that a planar configuration of 17 points, no 3 points collinear, always contains a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. ©  Australian MS