Block Sizes in Pairwise Balanced Designs
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 375-380
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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.
Colbourn, Charles J.; Phelps, Kevin T.; Rödl, Vojtěch. Block Sizes in Pairwise Balanced Designs. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 375-380. doi: 10.4153/CMB-1984-057-0
@article{10_4153_CMB_1984_057_0,
author = {Colbourn, Charles J. and Phelps, Kevin T. and R\"odl, Vojt\v{e}ch},
title = {Block {Sizes} in {Pairwise} {Balanced} {Designs}},
journal = {Canadian mathematical bulletin},
pages = {375--380},
year = {1984},
volume = {27},
number = {3},
doi = {10.4153/CMB-1984-057-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-057-0/}
}
TY - JOUR AU - Colbourn, Charles J. AU - Phelps, Kevin T. AU - Rödl, Vojtěch TI - Block Sizes in Pairwise Balanced Designs JO - Canadian mathematical bulletin PY - 1984 SP - 375 EP - 380 VL - 27 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-057-0/ DO - 10.4153/CMB-1984-057-0 ID - 10_4153_CMB_1984_057_0 ER -
%0 Journal Article %A Colbourn, Charles J. %A Phelps, Kevin T. %A Rödl, Vojtěch %T Block Sizes in Pairwise Balanced Designs %J Canadian mathematical bulletin %D 1984 %P 375-380 %V 27 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-057-0/ %R 10.4153/CMB-1984-057-0 %F 10_4153_CMB_1984_057_0
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