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Linear Spaces and Partitioning the Projective Plane

✍ Scribed by Ferenc Fodor

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 245 KB
Volume: 79
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2772

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✦ Synopsis

The aim of this paper is to settle a question about the partitioning of the projective plane by lines except for a small set. Suppose that Q is a set of points in the projective plane of order n and 6 is a set of lines that partitions the complement of Q. If Q has at most 2n&1 points and P has less than n+1+-n lines, then these lines are concurrent. An example is given which shows that the condition on the number of points of Q is sharp. However, it turns out that this is a 'pathological' example and if we exclude this case, then the statement can be improved. 1997 Academic Press The problem originates from a conjecture of de Witte [3], Erdo s, Mullin, So s and Stinson [2]. They conjectured that linear spaces with article no. TA962772 168 0097-3165Â97 25.00

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