Home > Combinatorics, Geometry > IMC 2014 Day 2 Problem 4

IMC 2014 Day 2 Problem 4


We say that a subset of {\Bbb{R}^n} is {k}almost contained by a hyperplane if there are less than {k} points in that set which do not belong to the hyperplane. We call a finite set of points {k}generic if there is no hyperplane that {k}-almost contains the set. For each pair of positive integers {k} and {n}, find the minimal number {d(k,n)} such that every finite {k}-generic set in {\Bbb{R}^n} contains a {k}-generic subset with at most {d(k,n)} elements.

IMC 2014 Day 2 Problem 4

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