Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-07-08T02:18:46.514Z Has data issue: false hasContentIssue false
  • English
  • Français

Triple systems with a fixed number of repeated triples

Part of: Designs and configurations

Published online by Cambridge University Press:  09 April 2009

C. A. Rodger
C. A. Rodger
Affiliation:
Department of Mathematics, Auburn University, Auburn, Alabama 36849, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

MSC classification

Secondary: 05B05: Block designs
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 180 - 187
Copyright
Copyright © Australian Mathematical Society 1986

References

[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.CrossRefGoogle Scholar
[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.+1’,+Canad.+Math.+Bull.,+to+appear.>Google Scholar
[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.CrossRefGoogle Scholar
[4]Cruse, A., ‘On embedding incomplete symmetric latin squares’, J. Combin. Theory Ser. A 16 (1974), 18–27.CrossRefGoogle Scholar
[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.Google Scholar
[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)).Google Scholar
[7]Hamm, R. C., ‘Embedding partial transitive triple systems’, Proc. 14th Southeastern Conf. on Combinatorics, Graph Theory and Computing, 1983, 447–453.Google Scholar
[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.Google Scholar
[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.CrossRefGoogle Scholar
[10]Lindner, C. C., ‘A survey of embedding theorems for Steiner systems’, Ann. Discrete Math. 7 (1980), 175–202.CrossRefGoogle Scholar
[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.Google Scholar
[12]Lindner, C. C. and Rosa, A., ‘Finite embedding theorems for partial Steiner triple systems’, Discrete Math. 13 (1975), 31–39.CrossRefGoogle Scholar
[13]Poucher, W. B., ‘Finite embedding theorems for partial pairwise balanced designs’, Discrete Math. 18 (1977), 291–298.CrossRefGoogle Scholar