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Some best possible bounds concerning the traces of finite sets

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Abstract

LetX be ann-element set and ℱ a family of its subsets. Considering the setsF∩(X - {x}) for a given x ∈X, there might be some coincidences, namely, ifF and G differ only in x, then they have the same intersection withX - {x}. It is proved that if |ℱ| ≤ 65n/14, then for an appropriatex ∈X, the number of coincidences is at most 9. Several similar, best possible bounds are obtained, continuing previous research by Bondy, Bollobás and the authors.

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Authors and Affiliations

  1. Department of Applied Mathematics, Science University of Tokyo, Kagurazaka, Shinjiku-ku, 162, Tokyo, Japan

    M. Watanabe

  2. CNRS, Paris, France

    P. Frankl

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  1. M. Watanabe
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  2. P. Frankl
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Watanabe, M., Frankl, P. Some best possible bounds concerning the traces of finite sets. Graphs and Combinatorics 10, 283–292 (1994). https://doi.org/10.1007/BF02986678

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  • DOI: https://doi.org/10.1007/BF02986678

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