benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let Z denote the set of points in R^(n) whose coordinates are 0 or 1. (Thus Z has 2^(n) elements, which are the vertices of a unit hypercube in R^(n).) Given a vector subspace V of…

Problem

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

problem

Let ZZ denote the set of points in Rn\mathbb{R}^n whose coordinates are 0 or 1. (Thus ZZ has 2n2^n elements, which are the vertices of a unit hypercube in Rn\mathbb{R}^n.) Given a vector subspace VV of Rn\mathbb{R}^n, let Z(V)Z(V) denote the number of members of ZZ that lie in VV. Let kk be given, 0≤k≤n0 \leq k \leq n. Find the maximum, over all vector subspaces V⊆RnV \subseteq \mathbb{R}^n of dimension kk, of the number of points in V∩ZV \cap Z.
Plain-text mathematical notation (without MathML)
Let Z denote the set of points in R^(n) whose coordinates are 0 or 1. (Thus Z has 2^(n) elements, which are the vertices of a unit hypercube in R^(n).) Given a vector subspace V of R^(n), let Z(V) denote the number of members of Z that lie in V. Let k be given, 0≤k≤n. Find the maximum, over all vector subspaces V⊆R^(n) of dimension k, of the number of points in V∩Z.
Original LaTeX notation
Let $Z$ denote the set of points in $\mathbb{R}^n$ whose coordinates are 0 or 1. (Thus $Z$ has $2^n$ elements, which are the vertices of a unit hypercube in $\mathbb{R}^n$.) Given a vector subspace $V$ of $\mathbb{R}^n$, let $Z(V)$ denote the number of members of $Z$ that lie in $V$. Let $k$ be given, $0 \leq k \leq n$. Find the maximum, over all vector subspaces $V \subseteq \mathbb{R}^n$ of dimension $k$, of the number of points in $V \cap Z$.

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
2de021fa-6791-58e1-9c4b-dc39c7e869a3
task_key
test--2de021fa-6791-58e1-9c4b-dc39c7e869a3
task_revision_id
1
config / split
/ test

Official source

initial import