TY - JOUR
T1 - Steiner triple systems with disjoint or intersecting subsystems
AU - Colbourn, Charles J.
AU - Oravas, Monica A.
AU - Rees, Rolf S.
PY - 2000
Y1 - 2000
N2 - The existence of incomplete Steiner triple systems of order v having holes of orders w and u meeting in z elements is examined, with emphasis on the disjoint (z = 0) and intersecting (z = 1) cases. When w ≥ u and v = 2w + u - 2z, the elementary necessary conditions are shown to be sufficient for all values of z. Then for z ∈ {0, 1} and v "near" the minimum of 2w + u - 2z, the conditions are again shown to be sufficient. Consequences for larger orders are also discussed, in particular the proof that when one hole is at least three times as large as the other, the conditions are again sufficient.
AB - The existence of incomplete Steiner triple systems of order v having holes of orders w and u meeting in z elements is examined, with emphasis on the disjoint (z = 0) and intersecting (z = 1) cases. When w ≥ u and v = 2w + u - 2z, the elementary necessary conditions are shown to be sufficient for all values of z. Then for z ∈ {0, 1} and v "near" the minimum of 2w + u - 2z, the conditions are again shown to be sufficient. Consequences for larger orders are also discussed, in particular the proof that when one hole is at least three times as large as the other, the conditions are again sufficient.
KW - Incomplete pairwise balanced design
KW - Steiner triple system
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U2 - 10.1002/(SICI)1520-6610(2000)8:1<58::AID-JCD8>3.0.CO;2-2
DO - 10.1002/(SICI)1520-6610(2000)8:1<58::AID-JCD8>3.0.CO;2-2
M3 - Article
AN - SCOPUS:27844569563
VL - 8
SP - 58
EP - 77
JO - Journal of Combinatorial Designs
JF - Journal of Combinatorial Designs
SN - 1063-8539
IS - 1
ER -