Allowable Sequences and Order Types in Discrete and Computational Geometry

TLDR: The allowable sequence associated to a configuration of points was first developed by the authors in order to investigate what combinatorial structure lay behind the Erdős-Szekeres conjecture (that any 2 n-2 + 1 points in general position in the plane contain among them n points which are in convex position) as mentioned in this paper.

Abstract: The allowable sequence associated to a configuration of points was first developed by the authors in order to investigate what combinatorial structure lay behind the Erdős-Szekeres conjecture (that any 2 n-2 + 1 points in general position in the plane contain among them n points which are in convex position) Though allowable sequences did not lead to any progress on this ancient problem, there did emerge an object that had considerable intrinsic interest, that turned out to be related to some other well-studied structures such as pseudoline arrangements and oriented matroids, and that had as well a combinatorial simplicity and suggestiveness which turned out to be effective in the solution of several other classical problems These connections and applications are discussed in Sections 2, 3, and 4 of this paper