Skip to main content
SpringerLink
Log in

The spectrum for large sets of pure directed triple systems

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Shen H. Embeddings of pure Mendelsohn triple systems and pure directed triple systems. J Combin Designs, 1995, 3(1): 41–50

    MATH  Google Scholar 

  2. Kang Q, Chang Y. A completion of the spectrum for large sets of transitive triple systems. J Combin Theory (A), 1992, 60: 287–294

    Article  MATH  MathSciNet  Google Scholar 

  3. Tian Z. On large sets and overlarge sets of combinatorial designs (in Chinese). Dissertation for the Doctoral Degree. Shijiazhuang: Hebei Normal University, 2003

    Google Scholar 

  4. Bennett F E, Kang Q, Lei J, et al. Large sets of disjoint pure Mendelsohn triple systems. J Statist Plann Inference, 2001, 95: 89–115

    Article  MATH  MathSciNet  Google Scholar 

  5. Lei J. Further results on large set of disjoint pure Mendelsohn triple systems. J Combin Designs, 2000, 8: 274–290

    Article  MATH  MathSciNet  Google Scholar 

  6. Mohácsy H, Ray-Chaudhuri D K. Candelabra systems and designs. J Statist Plann Inference, 2002, 106: 419–448

    Article  MATH  MathSciNet  Google Scholar 

  7. Kang Q, Tian Z. Large sets of oriented triple systems with resolvability. Discrete Math, 2000, 212: 199–221

    Article  MATH  MathSciNet  Google Scholar 

  8. Hanani H. On quadruple systems. Canad J Math, 1960, 12: 145–157

    MATH  MathSciNet  Google Scholar 

  9. Mills W H. On the covering of triples by quadruples. Congr Numer, 1974, 10: 563–581

    MathSciNet  Google Scholar 

  10. Mills W H. On the existence of H designs. Congr Numer, 1990, 79: 129–141

    MATH  MathSciNet  Google Scholar 

  11. Lei J. On large sets of Kirkman triple systems. Discrete Math, 2002, 257: 63–81

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Zhou Junling & Chang Yanxun

  2. Department of Mathematics, Suzhou University, Suzhou, 215006, China

    Ji Lijun

Authors
  1. Zhou Junling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chang Yanxun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ji Lijun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhou Junling.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, J., Chang, Y. & Ji, L. The spectrum for large sets of pure directed triple systems. SCI CHINA SER A 49, 1103–1127 (2006). https://doi.org/10.1007/s11425-006-2007-3

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-006-2007-3

Keywords

Search

Navigation