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On blocking sets of inversive planes

✍ Scribed by György Kiss; Stefano Marcugini; Fernanda Pambianco

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 96 KB
Volume: 13
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20037

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✦ Synopsis

Abstract

Let S be a blocking set in an inversive plane of order q. It was shown by Bruen and Rothschild 1 that |S| ≥ 2__q__ for q ≥ 9. We prove that if q is sufficiently large, C is a fixed natural number and |S = 2__q__ + C, then roughly 2/3 of the circles of the plane meet S in one point and 1/3 of the circles of the plane meet S in four points. The complete classification of minimal blocking sets in inversive planes of order q ≤ 5 and the sizes of some examples of minimal blocking sets in planes of order q ≤ 37 are given. Geometric properties of some of these blocking sets are also studied. © 2004 Wiley Periodicals, Inc.

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