MathDB

Let

Z

denote the set of points in

\mathbb{R}^{n}

whose coordinates are

0

1.

(Thus

Z

has

2^{n}

elements, which are the vertices of a unit hypercube in

\mathbb{R}^{n}

.) Given a vector subspace

V

\mathbb{R}^{n},

let

Z(V)

denote the number of members of

Z

that lie in

V.

Let

k

be given,

0\le k\le 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.

B4