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On a Conjecture of A. Hartman

  • S. Ajoodani-Namini
  • G. B. Khosrovshahi
Part of the Mathematics and Its Applications book series (MAIA, volume 329)

Abstract

We denote the complete design D (or the so-called trivial design) by \(S\left( {\left( {_{k - t}^{v - t}} \right);t,k,v} \right).\) A conjecture of Hartman states that one can partition D into two \(S\left( {\left( {_{k - t}^{v - t}} \right)/2;t,k,v} \right)\) designs if and only if \(\left( {_{k - i}^{v - i}} \right)\) is even for i = 0,...t. In this paper, some progress in support of the conjecture is reported.

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References

  1. [1]
    S. Ajoodani-Namini, All block designs with \( b = \left( {_k^v} \right)/2\) exist, 1994, submitted.Google Scholar
  2. [2]
    S. Ajoodani-Namini and G.B. Khosrovshahi, More on halving the complete designs, 1992, Discrete Math., in press.Google Scholar
  3. [3]
    W.O. Alltop, Extending t-designs, J. Combin. Theory, Ser. A 18 (1975), 177–186.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    A.Hartman, Halving the complete design, Ann. Discrete Math. 34 (1987), 207–224.MathSciNetGoogle Scholar
  5. [5]
    A.S. Hedayat, The theory of trade-off for t-design, in: Coding Theory and Design Theory, Part II, Design Theory (D.Ray-Chaudhuri, ed.), IMA Vol Math. Appl. 21, Springer-Verlag, 1990, 101–126.Google Scholar
  6. [6]
    A.S. Hedayat, G.B. Khosrovshahi, and D. Majumdar, A prospect for a general method for constructing t-designs, Discrete Appl. Math. 42 (1993), 31–50.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    G.B. Khosrovshahi and S. Ajoodani-Namini, An infinite family of 6-designs exists, Sankhyã 54 (1992), 259–264.MathSciNetzbMATHGoogle Scholar
  8. [8]
    G.B. Khosrovshahi and S. Ajoodani-Namini, A new basis for trades, SIAM J. Discrete Math. 3 (1990), 364–372.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • S. Ajoodani-Namini
    • 1
  • G. B. Khosrovshahi
    • 1
    • 2
  1. 1.Department of Mathematics 253-37California Institute of TechnologyPasadenaUSA
  2. 2.Institute for Studies in Theoretical Physics and Mathematics, and Department of MathematicsUniversity of TehranTehranIran

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