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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Archdeacon, Dan and Dinitz, Jeff 1993. Indecomposable triple systems exist for all lambda. Discrete Mathematics, Vol. 113, Issue. 1-3, p. 1.
    Gray, Ken 1990. On the minimum number of blocks defining a design. Bulletin of the Australian Mathematical Society, Vol. 41, Issue. 01, p. 97.
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Triple systems with a fixed number of repeated triples

  • C. A. Rodger (a1)
Abstract

In this paper, linear embeddings of partial designs into designs are found where no repeated blocks are introduced in the embedding process. Triple systems, pure cyclic triple systems, cyclic and directed triple systems are considered. In particular, a partial triple system with no repeated triples is embedded linearly in a triple system with no repeated triples.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1986
References
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[1]Andersen, L. D., Hilton, A. J. W. and Rodger, C. A., ‘A solution to the embedding problem for partial idempotent latin squares’, J. London Math. Soc. 26 (1982), 21–27.
[2]Colbourn, C. J., Hamm, R. C., Lindner, C. C. and Rodger, C. A., ‘Embedding partial graph designs, block designs and triple systems with λ > 1’, Canad. Math. Bull., to appear.
[3]Colbourn, C. J., Hamm, R. C. and Rodger, C. A., ‘Small embeddings of partial directed triple systems and partial triple systems with even γ’, J. Combin. Theory Ser. A 37 (1984), 363–369.
[4]Cruse, A., ‘On embedding incomplete symmetric latin squares’, J. Combin. Theory Ser. A 16 (1974), 18–27.
[5]diPaola, J. W. and Nemeth, E., ‘Generalized triple systems and medial quasigroups’, Proc. 7th Southeastern Conf. on Combinatorics, Graph Theory and Computing, 1976), 289–306.
[6]Hall, J. I. and Udding, J. T., ‘On intersection pairs of Steiner Triple Systems’, Indag Math. 39 (177), 87–100 ( = Proc. Konikl. Nederl. Akad. Wetensch. Ser. A 80 (1977)).
[7]Hamm, R. C., ‘Embedding partial transitive triple systems’, Proc. 14th Southeastern Conf. on Combinatorics, Graph Theory and Computing, 1983, 447–453.
[8]Hamm, R. C., Lindner, C. C. and Rodger, C. A., ‘Linear embeddings of partial directed triple systems with λ = 1 and partial triple systems with λ=2’, Ars Combin. 16 (1983), 11–16.
[9]Hilton, A. J. W., ‘Embedding an incomplete diagonal latin square in a complete diagonal latin square’, J. Combin. Theory Ser. A 15 (1973), 121–128.
[10]Lindner, C. C., ‘A survey of embedding theorems for Steiner systems’, Ann. Discrete Math. 7 (1980), 175–202.
[11]Lindner, C. C. and Evans, T., ‘Finite embedding theorems for partial designs and algebras’, Séminaires de Mathématiques Supérieures, 56, Les Presses de Accents l'Université de Montréal, Montréal, 1977.
[12]Lindner, C. C. and Rosa, A., ‘Finite embedding theorems for partial Steiner triple systems’, Discrete Math. 13 (1975), 31–39.
[13]Poucher, W. B., ‘Finite embedding theorems for partial pairwise balanced designs’, Discrete Math. 18 (1977), 291–298.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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