On blocking sets of inversive planes | Zendy

Kiss György | Zendy; Marcugini Stefano | Zendy; Pambianco Fernanda | Zendy

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On blocking sets of inversive planes

Author(s) -

Kiss György,

Marcugini Stefano,

Pambianco Fernanda

Publication year - 2005

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.20037

Subject(s) - mathematics , blocking (statistics) , combinatorics , plane (geometry) , blocking set , order (exchange) , set (abstract data type) , point (geometry) , discrete mathematics , geometry , pure mathematics , computer science , statistics , complex projective space , projective test , finance , projective space , economics , programming language

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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