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Blocking Sets in Desarguesian Affine and Projective Planes

✍ Scribed by Tamás Szőnyi

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
237 KB
Volume
3
Category
Article
ISSN
1071-5797

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✦ Synopsis

In this paper we show that blocking sets of cardinality less than 3(q ϩ 1)/2 (q ϭ p n ) in Desarguesian projective planes intersect every line in 1 modulo p points. It is also shown that the cardinality of a blocking set must lie in a few relatively short intervals. This is similar to previous results of Re ´dei, which were proved for a special class of blocking sets. In the particular case q ϭ p 2 , the above result implies that a nontrivial blocking set either contains a Baer-subplane or has size at least 3(q ϩ 1)/2; and this result is sharp. As a by-product, new proofs are given for the Jamison, Brouwer-Schrijver theorem on blocking sets in Desarguesian affine planes, and for Blokhuis' theorem on blocking sets in Desarguesian projective planes.

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