Abstract
An LPMTS(v,λ) is a collection of v−2λ disjoint pure Mendelsohn triple system PMTS(v,λ)s on the same set of v elements. An LPMTS⁎(v) is a special LPMTS(v,1) which contains exactly v−22 converse pairs of PMTS(v)s. In this paper, we mainly discuss the existence of an LPMTS⁎(v) for v≡6,10mod 12 and get the following conclusions: (1) there exists an LPMTS⁎(v) if and only if v≡0,4mod 6,v≥4 and v≠6. (2) There exists an LPMTS(v,λ) with index λ≡2,4mod 6 if and only if v≡0,4mod 6,v≥2λ+2,v≡2modλ.
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