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Bounding one-way differences

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Abstract

Letf(n, k) denote the maximum length of a sequence (F 1,F 2,...) of distinct subsets of ann-element set with the property that|F i ∖F j | < k for alli < j. We determine the exact values off(n, 2) and characterize all the extremal sequences. Fork ≥ 3 we prove that\(f(n,k) = (1 + o(1))\left( {\begin{array}{*{20}c} n \\ k \\ \end{array} } \right)\). Some related problems are also considered.

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Authors and Affiliations

  1. C.N.R.S. 15 Quai Anatole France, 75007, Paris, Cedex, France

    P. Frankl

  2. Mathematical Institute of the Hungarian Academy of Science, P.O. Box 127, 1364, Budapest, Hungary

    Z. Füredi & J. Pach

Authors
  1. P. Frankl
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  2. Z. Füredi
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  3. J. Pach
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Frankl, P., Füredi, Z. & Pach, J. Bounding one-way differences. Graphs and Combinatorics 3, 341–347 (1987). https://doi.org/10.1007/BF01788556

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  • DOI: https://doi.org/10.1007/BF01788556

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