The spectrum for large sets of pure directed triple systems

摘要

An LPDTS(υ) is a collection of 3(υ - 2) disjoint pure directed triple systems on the same set of υ elements. It is showed in Tian's doctoral thesis that there exists an LPDTS(υ) for υ ≡ 0,4 (mod 6), υ ≥ 4. In this paper, we establish the existence of an LPDTS(υ) for υ ≡ 1,3 (mod 6), υ > 3. Thus the spectrum for LPDTS(υ) is completely determined to be the set {υ : υ ≡ 0, 1 (mod 3), υ ≥ 4}.