MathDB

We say that a subset of

\mathbb{R}^n

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, n)

, find the minimal number of

d(k, n)

such that every finite

k

-generic set in

\mathbb{R}^n

contains a

k

-generic subset with at most

d(k, n)

elements.
(Proposed by Shachar Carmeli, Weizmann Inst. and Lev Radzivilovsky, Tel Aviv Univ.)

Problem Statement