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On the Nonuniform Fisher Inequality

✍ Scribed by László Babai

Publisher: Elsevier Science
Year: 1987
Tongue: English
Weight: 298 KB
Volume: 66
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90106-3

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✦ Synopsis

Let 3~ be a family of m subsets (lines) of a set of n elements (points). Suppose that each pair of lines has ~ points in common for some positive ~.. The Nonuniform Fisher Inequality asserts that under these circumstances m <~ n. We examine the case when m = n. We give a short proof of the fact that (with the exception of a trivial case) such an ~ must behave like a geometry in the following sense: a line must pass through each pair of points. This generalizes a result of de Bruijn and Erd6s.

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