文摘
An Erd?s–Ko–Rado set in a block design is a set of pairwise intersecting blocks. In this article we study Erd?s–Ko–Rado sets in \(2\,-\,(v,k,1)\) designs, Steiner systems. The Steiner triple systems and other special classes are treated separately. For \(k\ge 4\), we prove that the largest Erd?s–Ko–Rado sets cannot be larger than a point-pencil if \(r\ge k^{2}-3k+\frac{3}{4}\sqrt{k}+2\) and that the largest Erd?s–Ko–Rado sets are point-pencils if also \(r\ne k^{2}-k+1\) and \((r,k)\ne (8,4)\). For unitals we also determine an upper bound on the size of the second-largest maximal Erd?s–Ko–Rado sets.