A generalization of the Erdős–Ko–Rado theorem to [formula omitted]-designs in certain semilattices

Abstract

The Erdős–Ko–Rado theorem is extended to designs in semilattices with certain conditions. As an application, we show the intersection theorems for the Hamming schemes, the Johnson schemes, bilinear forms schemes, Grassmann schemes, signed sets, partial permutations and restricted signed sets.