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Recursive constructions and some properties of twofold designs with block size four

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

K. T. Phelps  and
A. Rosa
K. T. Phelps
Affiliation:
School of Mathematics Georgia Institute of TechnologyAtlanta, Georgia 30332, U.S.A.
A. Rosa
Affiliation:
Department of Mathematics and Statistics McMaster UniversityHamilton, OntarioCanadaL8S 4K1
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Abstract

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A direct construction for partially resolvable t-partitions is presented and then used to give a recursive construction for BIBDs (ν, 4, 2). In particular, we construct BIBD(ν, 4, 2) with BIBD(ν, 4, 2) embedded in it whenever ν = 3u + a, a ∈ {1, 4, 7}. This result allows us to give simple proofs for the existence of BIBD(ν, 4, 2) with various additioinal properties.

MSC classification

Secondary: 05B05: Block designs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 1 , February 1988 , pp. 64 - 70
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Billington, E. J., ‘Construction of some irreducible designs’, Combinat. Math. IX, pp. 182–196. (Lecture Notes in Math. 952, Springer, 1981).Google Scholar
[2]Billington, E. J., ‘Further constructions of irreducible designs’, Congr. Numer. 35 (1982), 77–89.Google Scholar
[3]Brouwer, A. E. and Andersen, L. D., personal communication.Google Scholar
[4]Hanani, H., ‘Balanced incomplete block designs and related designs’, Discrete Math. 11 (1975), 255–369.CrossRefGoogle Scholar
[5]Huang, C., Mendelsohn, E. and Rosa, A., ‘On partially resolvable t-partitions’, Ann. Discrete Math. 12 (1982), 169–183.Google Scholar
[6]Mathon, R. and Rosa, A., ‘Some results on the existence and enumeration of BIBDs’, Dept. of Math. and Stat., McMaster University, Mathematics Report 125-Dec-85.Google Scholar
[7]Ray-Chaudhuri, D. K. and Wilson, R. M., ‘Solution of Kirkman's schoolgirl problem’, Combinatorics, pp. 187–203 (Proc. Sympos. Pure Math., 19, Amer. Math. Soc. 1971).CrossRefGoogle Scholar
[8]Street, A. P., ‘A survey of irreducible balanced incomplete block designs’, Ars Combin. 19A (1985), 43–60.Google Scholar
[9]Lindner, C. C. and Street, A. P., ‘Disjoint designs and irreducible designs without repeated blocks’, Ars Combin. 21A (1986), 229–236.Google Scholar