Forbidden (0, 1)-vectors in hyperplanes of \(\mathbb{R}^n\): The restricted case
Denote \(E(n,k)\) the set of all \((0,1)\)-vectors in \(\mathbb{R}^n\) with exactly \(k\) ones. This paper tries to determine the maximum cardinality \(F(n,m,w)\) of \(X \subset E(n,m)\) such that the span \(\langle X\rangle\) does not contain any \((0,1)\)-vector with exactly \(w\) ones. The proofs use classical extremal set theoretical results, lengthy case analysis and calculations.
scientific article; zbMATH DE number 1968853