Directed Quadruple Designs

  • Nasrin Soltankhah
Part of the Mathematics and Its Applications book series (MAIA, volume 329)


A t-(v, k, λ) directed design (or simply a t-(v, k, λ)DD) is a pair (V, B), where V is a v-set and B is a collection of ordered k-tuples of distinct elements of V, such that every ordered t-tuple of distinct elements of V belongs to exactly λ elements of B. (We say that a t-tuple belongs to a k-tuple, if its components appear in that k-tuple as a set, and they appear with the same order.) In this paper we show that the necessary conditions for the existence of a 3-(v,4,1)DD are sufficient. Also for each even v and v ≡ 1,5,7 or 9 (mod 12) there exists a simple 3-(v, 4,2)DD. Also we exhibit a construction in the case when λ = 2.


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Nasrin Soltankhah
    • 1
  1. 1.Department of Mathematical SciencesSharif University of TechnologyTehranIran

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