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On Saturating Sets in Small Projective Geometries

✍ Scribed by Alexander A. Davydov; Patric R.J. Östergård

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
105 KB
Volume
21
Category
Article
ISSN
0195-6698

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✦ Synopsis

A set of points, S ⊆ P G (r, q), is said to be -saturating if, for any point x ∈ P G(r, q), there exist + 1 points in S that generate a subspace in which x lies. The cardinality of a smallest possible set S with this property is denoted by k(r, q, ). We give a short survey of what is known about k(r, q, 1) and present new results for k(r, q, 2) for small values of r and q. One construction presented proves that k(5, q, 2) ≤ 3q + 1 for q = 2, q ≥ 4. We further give an upper bound on k( + 1, p m , ).

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