A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belon...A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to A triples of B. An overlarge set of disjoint HTS（v, λ）, denoted by OLHTS（v, λ）, is a collection {（Y／{y}, .Ai）}i, such that Y is a （v ＋ 1）-set, each （Y／{y}, Ai） is an HTS（v, λ,） and all Ais form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS（v, A） and give the following conclusion： there exists an OLHTS（v, λ） if and only if λ= 1, 2, 4, v = 0, 1 （rood 3） and v ≥ 4.展开更多
基金Supported by the National Natural Science Foundation of China(No.10971051 and 11071056)
文摘A hybrid triple system of order v and index A, denoted by HTS（v, λ）, is a pair （X,B） where X is a v-set and B is a collection of cyclic triples and transitive triples on X, such that every ordered pair of X belongs to A triples of B. An overlarge set of disjoint HTS（v, λ）, denoted by OLHTS（v, λ）, is a collection {（Y／{y}, .Ai）}i, such that Y is a （v ＋ 1）-set, each （Y／{y}, Ai） is an HTS（v, λ,） and all Ais form a partition of all cyclic triples and transitive triples on Y. In this paper, we shall discuss the existence problem of OLHTS（v, A） and give the following conclusion： there exists an OLHTS（v, λ） if and only if λ= 1, 2, 4, v = 0, 1 （rood 3） and v ≥ 4.
