Nuclei of pointsets in \(PG(n,q)\). (English) Zbl 0892.51006
Let \(S\) be a set of points in \(PG(n,q)\) such that \(S\) does not contain a hyperplane and is not contained in the union of any \(t\) hyperplanes. A point \(P\notin S\) is a \(t\)-fold nucleus of \(S\) if each line through \(P\) contains at most (or at least) \(t\) points of \(S\) (depending on the size of \(S)\). This idea turns out to be related to the notion of blocking sets. The main result is an upper bound for the number of \(t\)-fold nuclei.
Reviewer: T.G.Ostrom (Pullman)
MSC:
| 51E20 | Combinatorial structures in finite projective spaces |
| 51E21 | Blocking sets, ovals, \(k\)-arcs |
References:
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| [3] | Blokhuis, A.; Wilbrink, H. A., A characterization of exterior lines of certain sets of points in PG \((2, q)\), Geom. Dedicata, 23, 253-254 (1987) · Zbl 0621.51013 |
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