摘要
A Mendelsohn triple system of order v (MTS(v)) is a pair (X,B) where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS(v) (X,B) is called pure and denoted by PMTS(v) if (x, y, z) ∈ B implies (z, y, x) ∈B. A large set of MTS(v)s (LMTS(v)) is a collection of v - 2 pairwise disjoint MTS(v)s on a v-set. A self-converse large set of PMTS(v)s, denoted by LPMTS* (v), is an LMTS(v) containing [ v-2/2] converse pairs of PMTS(v)s. In this paper, some results about the existence and non-existence for LPMTS* (v) are obtained.
A Mendelsohn triple system of order v (MTS(v)) is a pair (X,B) where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS(v) (X,B) is called pure and denoted by PMTS(v) if (x, y, z) ∈ B implies (z, y, x) ∈B. A large set of MTS(v)s (LMTS(v)) is a collection of v - 2 pairwise disjoint MTS(v)s on a v-set. A self-converse large set of PMTS(v)s, denoted by LPMTS* (v), is an LMTS(v) containing [ v-2/2] converse pairs of PMTS(v)s. In this paper, some results about the existence and non-existence for LPMTS* (v) are obtained.
基金
Supported by National Natural Science Foundation of China (Grant No.10771051)