منابع مشابه
On small blocking sets and their linearity
We prove that a small blocking set of PG(2, q) is “very close” to be a linear blocking set over some subfield GF(p) < GF(q). This implies that (i) a similar result holds in PG(n, q) for small blocking sets with respect to k-dimensional subspaces (0 ≤ k ≤ n) and (ii) most of the intervals in the interval-theorems of Szőnyi and Szőnyi-Weiner are empty.
متن کاملOn the Linearity of Higher-Dimensional Blocking Sets
A small minimal k-blocking set B in PG(n, q), q = pt, p prime, is a set of less than 3(qk + 1)/2 points in PG(n, q), such that every (n − k)-dimensional space contains at least one point of B and such that no proper subset of B satisfies this property. The linearity conjecture states that all small minimal k-blocking sets in PG(n, q) are linear over a subfield Fpe of Fq. Apart from a few cases,...
متن کاملCharacterization results on small blocking sets
In [8], De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 4; they proved that these blocking sets are truncated cones over the unique ovoid of Q+(7, 3). We continue this research by classifying all the minimal blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 3, of size at most 3n + 3n−2. This means that the three smallest minim...
متن کاملOn the stability of small blocking sets
A stability theorem says that a nearly extremal object can be obtained from an extremal one by “small changes”. In this paper, we study the relation of sets having few 0-secants and blocking sets.
متن کاملSmall 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= p. 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 dimen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2008
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2008.01.006