Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-13T23:55:18.491Z Has data issue: false hasContentIssue false
  • English
  • Français

Some New Replaceable Translation Nets

Published online by Cambridge University Press:  20 November 2018

A. A. Bruen
A. A. Bruen*
Affiliation:
University of Western Ontario, London, Ontario
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.

We discuss partial spreads (translation nets) U, V of ∑ = PG(3, q) where U, V cover the same points of ∑ and have no lines in common. Write t = |U| = |V|. It has been shown in a previous paper [4] that t ≧ 2(g — 1) provided q + 4.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 225 - 237
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Bruck, R. H., Construction problems of finite projective planes, Proceedings of the conference in combinatorics held at the University of North Carolina at Chapel Hill, April 10–14, 1967 (University of North Carolina Press, 1969).Google Scholar
2. Bruen, A., Spreads and a conjecture of Bruck and Bose, J. of Algebra 23 (1972), 519–537.Google Scholar
3. Bruen, A. Partial spreads and replaceable nets, Can. J. Math. 23 (1971), 381–391.Google Scholar
4. Bruen, A. and Silverman, R., Switching sets in PG﹛3, q), Proc. Amer. Math. Soc. 43 (1974), 176–180.Google Scholar
5. Foulser, D. A., Replaceable translation nets, Proc. London Math. Soc. 22 (1971), 235–264.Google Scholar
6. Hirschfeld, J. W. P., The double-six of lines over PG(3, 4), J. Aus. Math. Soc. 4 (1964), 83–89.Google Scholar
7. Johnson, N. L., A note on semi-translation planes of class I-5a, Archiv. Der Math. 21 (1970), 528–532.Google Scholar
8. Kleinfeld, E., Techniques for enumerating Veblen-Wedderburn systems, J. Assoc. Comput. Mach. 7 (1960), 330–337.Google Scholar
9. Pellegrino, G., Procedimenti geometrici per la costruzione di alcune classi di calotte complete in Sr,3, Bolletino U. M. I. 5 (1972), 109–115.Google Scholar