On large sets of hybrid triple systems

Abstract

An oriented triple system B on a ν-set X is called an HTS(ν,λ) if it contains both cyclic and transitive triples such that each ordered pair of distinct elements is contained in exactly λ triples of B . If all the cyclic and transitive triples from X can be partitioned into ∪ r B r such that each (X, B r is an HTS( ν, λ), then {(X, B r} r is called an LHTS(ν,λ). In this paper, the existence spectrum of LHTS(ν,λ) is completed, that is 4( ν − 2) ≡ 0 (mod λ), 4( ν − 2) ⩾ λ, if λ ≉ 0 (mod 3) then ν ≉ 2 (mod 3) and if λ = 1 then ν ≠ 3.