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Block Sizes in Pairwise Balanced Designs

Published online by Cambridge University Press:  20 November 2018

Charles J. Colbourn ,
Kevin T. Phelps  and
Vojtěch Rödl
Charles J. Colbourn
Affiliation:
Department of Computational Science, University of Saskatchewan, Saskatoon, Saskatchewan S7N 0W0, Canada
Kevin T. Phelps
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.
Vojtěch Rödl
Affiliation:
FJFI, CVUT, Husova 5, Praha 1, Czechoslovakia
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Abstract

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The number of sets of integers which are realizable as block sizes of a pairwise balanced design of order n is between and ; in contrast, when the multiplicity of each block size is also specified, the number of multisets which can be realized is between and . Although this gives a reasonable bound on the number of multisets which can be realized, a good characterization is not likely to exist; deciding whether a multiset can be so realized is NP-complete.

Keywords

05B3005B05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 375 - 380
Copyright
Copyright © Canadian Mathematical Society 1984

References

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5. Vanstone, S. A., The extendibility of (r, 1) designs, Proceedings of the Third Manitoba Conference on Numerical Mathematics and Computing, 1973.Google Scholar