benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / We say that a subset of 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 point…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

We say that a subset of Rn\mathbb{R}^{n} is kk-almost contained by a hyperplane if there are less than kk points in that set which do not belong to the hyperplane. We call a finite set of points kk-generic if there is no hyperplane that kk-almost contains the set. For each pair of positive integers kk and nn, find the minimal number d(k,n)d(k, n) such that every finite kk-generic set in Rn\mathbb{R}^{n} contains a kk-generic subset with at most d(k,n)d(k, n) elements.
Plain-text mathematical notation (without MathML)
We say that a subset of 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 R^(n) contains a k-generic subset with at most d(k,n) elements.
Original LaTeX notation
We say that a subset of $\mathbb{R}^{n}$ 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 $\mathbb{R}^{n}$ contains a $k$-generic subset with at most $d(k, n)$ elements.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
4ebaad35-a1ec-5254-b902-40e552029c02
task_key
test--4ebaad35-a1ec-5254-b902-40e552029c02
task_revision_id
1
config / split
/ test

Official source

initial import