The directed packing numbersDD(t, v, v), t≧4


A directed packing is a maximal collection ofk-subsets, called blocks, of a set of cardinalityv having the property that no orderedt-subset occurs in more than one block. A block contains an orderedt-set if its symbols appear, left to right, in the block. The cardinality of such a maximal collection is denoted byDD(t, k, v). We consider the special case whenk=v and derive some results on the sizes of maximal collections.

This is a preview of subscription content, access via your institution.


  1. [1]

    P. Erdös andG. Szekerfs, A Combinatorial Problem in Geometry,Compositio Mathemativa 2 (1935), 463–470.

    MATH  Google Scholar 

  2. [2]

    R. G. Stanton andD. B. Skillicorn, The Directed Packing NumbersDD(3,v, v),Proceedings of 11th Manitoba Conference on Numerical Mathematics and Computing, to appear.

  3. [3]

    D. B. Skillicorn,Directed Packings and Coverings with Computer Applications, Ph. D. Thesis, University of Manitoba, 1981.

  4. [4]

    J. E. Dawson, Algorithms to find directed packings,Annals of Discrete Mathematics, to appear.

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dawson, J.E., Skillicorn, D.B. & Seberry, J. The directed packing numbersDD(t, v, v), t≧4. Combinatorica 4, 121–130 (1984).

Download citation

AMS subject classification (1980)

  • 05 B 40