Extremal t-intersecting families for direct products.

In this paper, by shifting technique we study t -intersecting families for direct products where the ground set is divided into several parts. Assuming the size of each part is sufficiently large, we determine all extremal t -intersecting families for direct products. We also prove that every largest t -intersecting subfamily of a more general family introduced by Katona is trivial under certain conditions. [ABSTRACT FROM AUTHOR]