Non-intersecting broken lines
Source: Iran TST 2012-Third exam-2nd day-P5
May 16, 2012
rotationinequalitiescombinatorial geometrycombinatorics proposedcombinatorics
Problem Statement
Let be a natural number. Suppose and are two sets, each containing points in the plane, such that no three points of a set are collinear. Let be the number of broken lines, each containing segments, and such that it doesn't intersect itself and its vertices are points of . Define similarly. If the points of are vertices of a convex -gon (are in convex position), but the points of are not, prove that .Proposed by Ali Khezeli