Blocking sets and partial spreads in finite projective spaces

1980 ◽  
Vol 9 (4) ◽  
Author(s):  
Albrecht Beutelspacher
Keyword(s):  
Projective Spaces ◽  
Blocking Sets ◽  
Partial Spreads ◽  
Finite Projective Spaces

Blocking Sets and Skew Subspaces of Projective Space

1980 ◽  
Vol 32 (3) ◽  
pp. 628-630 ◽  
Author(s):  
Aiden A. Bruen
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Projective Spaces ◽  
Higher Dimensions ◽  
Blocking Set ◽  
Blocking Sets ◽  
Partial Spreads ◽  
Dimension One

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].

Blocking Sets in Projective Spaces

1978 ◽  
Vol 30 (4) ◽  
pp. 856-862
Author(s):  
Gary L. Ebert
Keyword(s):  
Game Theory ◽  
Projective Plane ◽  
Projective Spaces ◽  
Blocking Set ◽  
Blocking Sets ◽  
Partial Spreads ◽  
Image Position

Blocking sets in projective spaces have been of interest for quite some time, having applications to game theory (see [6; 7]) as well as finite nets and partial spreads (see [5]). In [4] Bruen showed that if B is a blocking set in a projective plane of order n, then

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