Skip to main content
SpringerLink
Log in

Kirkman frames having hole type h u m 1 for small h

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

We begin an investigation into the spectrum of (non-uniform) Kirkman frames of type h u m 1, paying particular attention to the cases where h ∈{2,4,6,8,10,12}. We show that for each of these values of h the obvious necessary conditions on u, m are sufficient in all but at most 24 cases of (h,u,m).

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. Beth T, Jungnickel D and Lenz H (1999). Design theory, 2nd edn. Cambridge University Press, Cambridge, UK

    Google Scholar 

  2. Colbourn CJ and Dinitz JH (1996). CRC handbook of combinatorial designs. CRC Press, Boca Raton, FL

    MATH  Google Scholar 

  3. Colbourn CJ, Hoffman DG and Rees RS (1992). A new class of group-divisible designs with block size three. J Comb Theory Ser A 59: 73–89

    Article  MATH  MathSciNet  Google Scholar 

  4. Furino SC, Miao Y and Yin J (1996). Frames and resolvable designs. CRC Press, Boca Raton, FL

    MATH  Google Scholar 

  5. Ge G and Ling ACH (2004). Group divisible designs with block size four and group type g u m 1 with small g. Discrete Math 285: 97–120

    Article  MATH  MathSciNet  Google Scholar 

  6. Ge G and Rees RS (2002). On group-divisible designs with block size four and group-type g u m 1. Des Codes Cryptogr 27: 5–24

    Article  MATH  MathSciNet  Google Scholar 

  7. Ge G and Rees RS (2004). On group-divisible designs with block size four and group-type 6u m 1. Discrete Math 279: 247–265

    Article  MATH  MathSciNet  Google Scholar 

  8. Ge G, Rees RS and Zhu L (2002). Group-divisible designs with block size four and group-type g u m 1 with m as large or as small as possible. J Comb Theory Ser A 98: 357–376

    Article  MATH  MathSciNet  Google Scholar 

  9. Ge G and Wei R (2004). HGDDs with block size four. Discrete Math 279: 267–276

    Article  MATH  MathSciNet  Google Scholar 

  10. Rees RS and Stinson DR (1989). On the existence of incomplete designs of block size four having one hole. Utilitas Math 35: 119–152

    MATH  MathSciNet  Google Scholar 

  11. Stinson DR (1987). Frames for Kirkman triple systems. Discrete Math 65: 289–300

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, Zhejiang, P. R. China

    Gennian Ge

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada, A1C 5S7

    Rolf Rees & Nabil Shalaby

Authors
  1. Gennian Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rolf Rees
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nabil Shalaby
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gennian Ge.

Additional information

Communicated by C. J. Colbourn.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ge, G., Rees, R. & Shalaby, N. Kirkman frames having hole type h u m 1 for small h . Des. Codes Cryptogr. 45, 157–184 (2007). https://doi.org/10.1007/s10623-007-9105-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-007-9105-2

Keywords

AMS Classification

Search

Navigation