Constructions for overlarge sets of disjoint pure directed triple systems

摘要

Let X be a v-set, v≥3. A transitive triple (x,y,z) on X is a set of three ordered pairs (x,y),(y,z) and (x,z) of X. A directed triple system of order v, denoted by DTS(v), is a pair (X,B), where X is a v-set and B is a collection of transitive triples on X such that every ordered pair of X belongs to exactly one triple of B. A DTS(v) is called pure and denoted by PDTS(v) if (x,y,z) B implies (z,y,x)?B. An overlarge set of disjoint PDTS(v) is denoted by OLPDTS(v). In this paper, we establish some recursive constructions for OLPDTS(v), so we obtain some results.