TY - JOUR
T1 - Percentages in Pairwise Balanced Designs
AU - Colbourn, Charles J.
AU - Rötdl, Vojtech
N1 - Funding Information:
Thanks to Alex Rosa for suggesting this problem, and to Kevin Phelps for helpful discussions. Research of the first author is supported by NSERC Canada under grant A0579.
PY - 1989/1/1
Y1 - 1989/1/1
N2 - Let K ={K1,…, km} be a set of block sizes, and let {p1,…, pm} be nonnegative numbers with Σmi=1, pi We prove the following theorem: for any ε>0, if a (v, K, 1) pairwise balanced design exists and v is sufficiently large, then a (v, K, 1) pairwise balanced design exists in which the fraction of pairs appearing in blocks of size kiis pi,±ε for every i. We also show that the necessary conditions for a pairwise balanced design having precisely the fraction pi, of its pairs in blocks of size ki for each i are asymptotically sufficient.
AB - Let K ={K1,…, km} be a set of block sizes, and let {p1,…, pm} be nonnegative numbers with Σmi=1, pi We prove the following theorem: for any ε>0, if a (v, K, 1) pairwise balanced design exists and v is sufficiently large, then a (v, K, 1) pairwise balanced design exists in which the fraction of pairs appearing in blocks of size kiis pi,±ε for every i. We also show that the necessary conditions for a pairwise balanced design having precisely the fraction pi, of its pairs in blocks of size ki for each i are asymptotically sufficient.
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U2 - 10.1016/S0167-5060(08)70097-9
DO - 10.1016/S0167-5060(08)70097-9
M3 - Article
AN - SCOPUS:77957073560
SN - 0167-5060
VL - 42
SP - 57
EP - 63
JO - Annals of Discrete Mathematics
JF - Annals of Discrete Mathematics
IS - C
ER -