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Computer solution to the 17-point Erdős-Szekeres problem

  • George Szekeres (a1) and Lindsay Peters (a2)
  • DOI: http://dx.doi.org/10.1017/S144618110000300X
  • Published online: 01 February 2009
Abstract
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We describe a computer proof of the 17-point version of a conjecture originally made by Klein-Szekeres in 1932 (now commonly known as the “Happy End Problem”) that a planar configuration of 17 points, no 3 points collinear, always contains a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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]W. E. Bonnice , “On convex polygons determined by a finite planar set”, Amer. Math. Monthly 81 (1974) 749752.

[2]F. R. K. Chung and R. L. Graham , “Forced convex n-gons in the plane”, Discrete Comput. Geom. 19 (1998) 367371, Special Issue.

[6]D. E. Knuth , Axioms and Hulls (Springer, Heidelberg, 1992).

[7]W. Morris and V. Soltan , “The Erdős-Szekeres problem on points in convex position. A survey”, Bull. Amer. Math. Soc. (N.S.) 37 (2000) 437458.

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The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
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