Forbidding just one intersection |
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Authors: | Peter Frankl Zoltán Füredi |
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Affiliation: | CNRS, 15 Quai Anatole France, Paris 75007, France;Math Institute, Hungarian Academy of Science, 1364 Budapest, P.O.B. 127, Hungary |
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Abstract: | Following a conjecture of P. Erdös, we show that if is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ? 2l + 2 and n sufficiently large || ? (k ? l ? 1n ? l ? 1) with equality holding if and only if consists of all the k-sets containing a fixed (l + 1)-set. In general we show || ? dknmax;{;l,k ? l ? 1};, where dk is a constant depending only on k. These results are special cases of more general theorems (Theorem 2.1–2.3). |
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