Zsuzsa Weiner

Small Blocking Sets in Higher Dimensions

We show that small blocking sets in PG(n, q) with respect to hyperplanes intersect every hyperplane in 1 modulo p points, where q=ph. The result is then extended to blocking sets with respect to k-dimensional subspaces and, at least when p>2, to intersections with arbitrary subspaces not just hyperplanes. This can also be used to characterize certain non-degenerate blocking sets in higher dimensions. Furthermore we determine the possible sizes of small minimal blocking sets with respect to k-dimensional subspaces.

On 1-Blocking Sets in PG(n,q), n≥3

In this article we study minimal1-blocking sets in finite projective spaces PG(n,q),n ≥ 3. We prove that in PG(n,q2),q = ph, p prime, p > 3,h ≥ 1, the second smallest minimal 1-blockingsets are the second smallest minimal blocking sets, w.r.t.lines, in a plane of PG(n,q2). We also study minimal1-blocking sets in PG(n,q3), n ≥ 3, q = ph, p prime, p > 3,q ≠ 5, and prove that the minimal 1-blockingsets of cardinality at most q3 + q2 + q + 1 are eithera minimal blocking set in a plane or a subgeometry PG(3,q).

On ( q + t , t )-Arcs of Type (0, 2, t )

In this paper we construct an infinite series of (q + t, t)-arcs of type (0, 2, t). We show that this construction includes the Korchmáros-Mazzocca arcs, and we gain new infinite series of examples, too.

On q-analogues and stability theorems

In this survey recent results about q-analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q-analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.

On Sets without Tangents in Galois Planes of Even Order

AbstractWe show that the cardinality of a nonempty set of points without tangents in the desarguesian projective plane PG(2, q), q even, is at least q + 1 +

On the Representability of the Biuniform Matroid

\sqrt {q/6}

On the spectrum of minimal blocking sets in PG

provided that the set is not of even type.

(2,q)

In this paper we prove that a point set of size less than