On the Existence of (3,lambda)-Semiframes of Type 3(u)

摘要

A (k,lambda)-semiframe of type g(u) is a (k,lambda)-group-divisible design of type g(u) (X, G, B), in which the collection of blocks B can be written as a disjoint union B = P U L where L is partitioned into parallel classes of X and P is partitioned into holey parallel classes, each holey parallel class being a partition of XG(j) for some G(j) is an element of G. In this paper, we shall prove that the necessary conditions for (3,lambda)-semiframes of type 3(u) are also sufficient with one exception.