Skip to main content
SpringerLink
Log in

Anti-mitre steiner triple systems

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

A mitre in a Steiner triple system is a set of five triples on seven points, in which two are disjoint. Recursive constructions for Steiner triple systems containing no mitre are developed, leading to such anti-mitre systems for at least 9/16 of the admissible orders. Computational results for small cyclic Steiner triple systems are also included.

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. Brouwer, A.E.: Steiner triple systems without forbidden subconfigurations, Mathematisch Centrum Amsterdam, ZW 104–77, 1977

  2. Colbourn, M.J., Mathon, R.: On cyclic Steiner 2-designs, Ann. Discrete Math.7, 215–253 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Frenz, T.C., Kreher, D.L.: An algorithm for enumerating distinct cyclic Steiner systems, J. Comb. Math. Comb. Comput.11, 23–32 (1992)

    MATH  MathSciNet  Google Scholar 

  4. Griggs, T.S., Murphy, J., Phelan, J.S.: Anti-Pasch Steiner triple systems, J. Comb. Inf. Syst. Sci.15, 79–84 (1990)

    MATH  MathSciNet  Google Scholar 

  5. Lefmann, H., Phelps, K.T., Rödl, V.: Extremal problems for triple systems, J. Combinat. Designs1, 379–394 (1993)

    Article  MATH  Google Scholar 

  6. Mathon, R., Phelps, K.T., Rosa, A.: Small Steiner triple systems and their properties, Ars Comb.15, 3–110 (1983)

    MATH  MathSciNet  Google Scholar 

  7. Robinson, R.M.: The structure of certain triple systems, Math. Comput.20, 223–241 (1975)

    Google Scholar 

  8. Rosa, A.: Algebraic properties of designs and recursive constructions, Congressus Numer.13, 183–200 (1975)

    Google Scholar 

  9. Stinson, D.R., Wei, R.: Some results on quadrilaterals in Steiner triple systems, Discrete Math.105, 207–219 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Street, A.P., Street, DJ.: The Combinatorics of Experimental Design, Clarendon Press, Oxford, 1987

    Google Scholar 

  11. Teirlinck, L.: Large sets of disjoint designs and related structures, in: Contemporary Design Theory (J.H. Dinitz and D.R. Stinson, eds.) Wiley, New York, 1992, pp. 561–592

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Combinatorics and Optimization, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Charles J. Colbourn

  2. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

    Eric Mendelsohn

  3. Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    Alexander Rosa

  4. Katedra algebry a teórie čísel, Univerzita Komenského, 84215, Bratislava, Slovakia

    Jozef Širáň

Authors
  1. Charles J. Colbourn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eric Mendelsohn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Rosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jozef Širáň
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colbourn, C.J., Mendelsohn, E., Rosa, A. et al. Anti-mitre steiner triple systems. Graphs and Combinatorics 10, 215–224 (1994). https://doi.org/10.1007/BF02986668

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02986668

Keywords

Search

Navigation