1,721,178 research outputs found
Special point sets in PG(n,q) and the structure of sets with the maximal number of nuclei
No full text
On two-intersection sets with respect to hyperplanes in projective spaces
No full textIn \cite{BLLA} a construction of a class of two-intersection sets with respect
to hyperplanes in , even, is given, with
the same parameters as the union of disjoint
Baer subgeometries if is even and the union of elements
of an -spread in if is odd. In this paper we prove
that although they have the same parameters, they are different.
This was previously proved in \cite{BABLLA} in the special case where and
Scattered spaces with respect to a spread in PG(n,q)
No full textA scattered subspace of with respect to a -spread is
a subspace intersecting every spread element in at most a point.
Upper and lower bounds for the dimension of a maximum scattered space are given.
In the case of a normal spread new classes of two intersection sets with
respect to hyperplanes in a projective space are
obtained using scattered spaces
On the classification of semifield flocks
No full textIt is shown that the only semifield flocks of the quadratic cone of
with
are the linear flocks and the Kantor-Knuth semifield flocks. This follows
from the main theorem which states that there are no subplanes of order
contained in the set of internal points of a conic in for those
exceeding the bound
The Kakeya problem: a gap in the spectrum and classification of the smallest examples
No full textThe authors present a new example of a small Kakeya set in the affine plane AG(2,q) and they give the classification of the smallest Kakeya sets with at most 1/2q(q+2)+q/4 points, in case q even
Linear -fold blocking sets in {\rm PG}(2,q\sp4).
No full textA -fold blocking set of size in is constructed,
which is not the union of disjoint Baer subplanes
The finite field Kakeya problem
No full textA Besicovitch set in AG(n; q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n > 4
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