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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

On a Problem of Hartman and Heinrich Concerning Pairwise Balanced Designs with Holes

Yeow Meng Chee 1, Charles J. Colbourn2, Robert P. Gallant2, Alan C. H. Ling2
1Department of Computer Science University of Waterloo Waterloo, Ontario Canada N2L 3G1
2Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario Canada N2L 3G1

Abstract

We consider the problem of constructing pairwise balanced designs of order \(v\) with a hole of size \(k\). This problem was addressed by Hartman and Heinrich who gave an almost complete solution. To date, there remain fifteen unresolved cases. In this paper, we construct designs settling all of these.

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Citation
Yeow Meng Chee , Charles J. Colbourn, Robert P. Gallant, Alan C. H. Ling. On a Problem of Hartman and Heinrich Concerning Pairwise Balanced Designs with Holes[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 023. 121-127. DOI: .