Large Sets Of Oriented Packing Triple Systems

A directed (resp., Mendelsohn) packing triple system of order v, briefly DPT(v)(resp., MPT(v)), is a pair (X,B) where X is a v-set and B is a collection of transitive (resp., cyclic) triples on X such that every ordered pair of X belongs to at most one triple of B. An LDPT(v)(resp., LMPT(v)) is a large set consisting of3(v-3)(resp., v-3) disjoint compatible DPT(v)s (resp., MPT(v)s) with a2-cycle as the common leave.In this paper, we discuss the existence problem of LDPT(v)(resp., LMPT(v)). The dissertation is divided into five chapters as follows.In Chapter1, we introduce some basic concepts and background of large sets of oriented packing triple systems.In Chapter2, we introduce some recursive constructions, basic concepts and known results in the use of recursive constructions.In Chapter3, we completely determine the existence spectrum of directed packing triple systems:there exists an LDPT(v) if and only if v≡2(mod3), v≥5.In Chapter4, we discuss the existence problem of LMPT(v) and give the following conclusions:if v≡14(mod18), there exists an LMPT(v); there exists no an LMPT(8).In Chapter5, we propose some problems of large sets of oriented packing triple systems for further research.