Abstract
A Mendelsohn triple system of order υ (MTS(υ)) is a pair (X, ℬ) where X is a υ-set and ℬ is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of ℬ. An MTS(υ) (X, ℬ) is called pure and denoted by PMTS(υ) if 〈x, y, z〉 ∈ ℬ implies 〈z, y, x〉 ∉ ℬ. A large set of MTS(υ)s (LMTS(υ)) is a collection of υ − 2 pairwise disjoint MTS(υ)s on a υ-set. A self-converse large set of PMTS(υ)s, denoted by LPMTS*(υ), is an LMTS(υ) containing ⌎υ−2/2⌏ converse pairs of PMTS(υ)s. In this paper, some results about the existence and non-existence for LPMTS*(υ) are obtained.
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