Abstract

Abstract In this and the next chapter, we examine extemions of designs (particularly triple systems), in which blocks are taken to contain orderedrather than unordered pairs. Vieprimarily consider two different types of ordered blocks. The transitive triple(a,b,c) is said to contain the ordered pairs (a,b),(a,c) and (b,c).The cyclic triple(a, b,c)contains the ordered pairs (a,b), (b,c)and (c, a). We examine directed triple systems in which the blocks are transitive triples, Mendelsohn triple systems in which the blocks are cyclic triples, and hybrid triple systems in which the blocks are permitted to be either.

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