Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-06T23:09:27.864Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximal Strictly Partial Spreads

Published online by Cambridge University Press:  20 November 2018

Gary L. Ebert
Gary L. Ebert*
Affiliation:
Texas Tech University, Lubbock, Texas; University of Delaware, Newark, Delaware
Rights & Permissions [Opens in a new window]

Extract

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.

Let ∑ = PG(3, q) denote 3-dimensional projective space over GF(q). A partial spread of ∑ is a collection W of pairwise skew lines in ∑. W is said to be maximal if it is not properly contained in any other partial spread. If every point of ∑ is contained in some line of W, then W is called a spread. Since every spread of PG(3, q) consists of q2 + 1 lines, the deficiency of a partial spread W is defined to be the number d = q2 + 1 — |W|. A maximal partial spread of ∑ which is not a spread is called a maximal strictly partial spread (msp spread) of ∑.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 3 , 01 June 1978 , pp. 483 - 489
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Andrews, G. E., Number theory (W. Saunders, B. , Philadelphia, London, Toronto, 1971)Google Scholar
2. Bruck, R. H., Construction problems of finite projective planes, Combinatorial Mathematics and Its Applications, ed. Bose, R. C. and Dowling, T. A., The University of North Carolina Press, Chapel Hill (1969), 426–104.Google Scholar
3. Bruen, A., Partial spreads and replaceable nets, Can. J. Math. 381-391 (1971), 381-391.Google Scholar
4. Bruen, A. A. and Hirschfeld, J. W. P., Applications of line geometry over finite fields I. The twisted cubic, Geometriae Dedicata, to appear.Google Scholar
5. Buell, D. A. and Williams, K. S., Maximal residue difference sets modulo p, Proc. Amer. Math. Soc, to appear.Google Scholar
6. Dembowski, P., Finite geometries (Springer-Verlag, Berlin, 1968).Google Scholar
7. Orr, W. F., The miquelian inversive plane IP(q) and the associated projective planes, Dissertation, University of Wisconsin, Madison, Wisconsin, 1973.Google Scholar
8. Wilson, R. M., Cyclotomy and difference families in elementary abelian groups, J. Number Theory 4 (1972), 17–47.Google Scholar