Maximum number of constant weight vertices of the unit \(n\)-cube contained in a \(k\)-dimensional subspace
The largest intersection \(| U\cap E(n,w)| \) is determined where \(U\) is a \(k\)-dimensional subspace of \(\mathbb{R}^n\) and \(E(n,w)\) is the set of length-\(n\) 0-1 sequences with \(w\) 1-entries. It is \(k \choose w\) for \(w\leq k/2\), \({{2(k-w)} \choose {k-w}}2^{2w-k}\) for \(k/2<w<k-1\), and \(2^{k-1}\) for \(k-1\leq w \leq n/2\). An extension of Erdős-Moser type and one on multisets are also given.
scientific article; zbMATH DE number 2099001