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Block Sizes in Pairwise Balanced Designs
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1984
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