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An infinite class of fibres in CURDs with block sizes two and three
Author(s) -
Keranen Melissa S.,
Rees Rolf S.,
Ling Alan C.H.
Publication year - 2003
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.10053
Subject(s) - mathematics , combinatorics , block (permutation group theory) , class (philosophy) , discrete mathematics , computer science , artificial intelligence
Class‐uniformly resolvable designs (CURDs) are introduced by Lamken et al. Discrete Math 92 (1991) 197–209. In Wevrick and Vanstone, J Combin Designs 4 (1996) 177–202, a classification scheme is developed based on the ratio a : b of pairs to triples. Asymptotic existence results are obtained when ( a , b ) = (1,2 n ), n ≥ 1 and when ( a , b ) = (9,2). The authors also obtain partial results on the existence of CURDs when ( a , b ) = (1,2 n ), 1 ≤ n ≤ 5, ( a , b ) = (3, 6 u − 2), u ≥ 1 and when ( a , b ) ∈ {(1,1), (3,1), (7,2), (3,4), (9,2)}. In Danziger and Stevens, J Combin Designs 9 (2001), 79–99, the necessary and sufficient conditions for CURDs when ( a , b ) = (3,1) are completely settled. In this article, we obtain a necessary and sufficient condition when ( a , b ) = (3 m , 1) for all m > 1. © 2003 Wiley Periodicals, Inc.