Frankl, Peter; Kupavskii, Andrey Families of vectors without antipodal pairs. (English) Zbl 1413.05369 Stud. Sci. Math. Hung. 55, No. 2, 231-237 (2018). Let \(V(n,k,l)\) stand for the set of all \((v_{1},\dots,v_{n})\) vectors whose \(k\) coordinates equal \(1,\) \(l\) coordinates equal \(-1,\) with the remaining ones equal to \(0\). Clearly, the scalar product \(\langle u,v\rangle =\sum_{i=1}^{n}u_{i}v_{i}\) of two vectors from \(V(n,k,l)\) is \(\geq -2l\). Two vectors are called antipodal if their scalar product is equal to \(-2l\). In the paper, an asymptotically best possible bound on the size of a largest subset of \(V(n,k,l)\) containing no pair of antipodal vectors is given. Reviewer: Peter Horák (Tacoma) Cited in 7 Documents MSC: 05D05 Extremal set theory 05C65 Hypergraphs Keywords:antipodal pairs; Erdős-Ko-Rado theorem; families of vectors PDFBibTeX XMLCite \textit{P. Frankl} and \textit{A. Kupavskii}, Stud. Sci. Math. Hung. 55, No. 2, 231--237 (2018; Zbl 1413.05369) Full Text: DOI arXiv Link