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Blocking Sets and Skew Subspaces of Projective Space

Published online by Cambridge University Press:  20 November 2018

Aiden A. Bruen
Aiden A. Bruen*
Affiliation:
University of Western Ontario, London, Ontario
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In what follows, a theorem on blocking sets is generalized to higher dimensions. The result is then used to study maximal partial spreads of odd-dimensional projective spaces.

Notation. The number of elements in a set X is denoted by |X|. Those elements in a set A which are not in the set Bare denoted by A — B. In a projective space Σ = PG(n, q) of dimension n over the field GF(q) of order q, ┌d(Ωd, Λd, etc.) will mean a subspace of dimension d. A hyperplane of Σ is a subspace of dimension n — 1, that is, of co-dimension one.

A blocking set in a projective plane π is a subset S of the points of π such that each line of π contains at least one point in S and at least one point not in S. The following result is shown in [1], [2].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 3 , 01 June 1980 , pp. 628 - 630
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Bruen, A., Baer subplanes and blocking sets, Bull. Amer. Math. Soc. 76 (1970), 342–344.Google Scholar
2. Bruen, A., Blocking sets infinite projective planes, SIAM. J. Appl. Math. 21 (1971), 380–392.Google Scholar
3. Bruen, A., Collineations and extensions of translation nets, Math. Z. 145 (1975), 243–249.Google Scholar
4. Bruen, A. and Thas, J. A., Blocking sets, Geom. Ded. 6 (1977), 193–203.Google Scholar