Counterexample to the Frankl-Pach conjecture for uniform, dense families

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References

  1. [1]

    N. Sauer: On the density of families of sets,J. Comb. Th. (A) 13 (1972), 145–147.

    Google Scholar 

  2. [2]

    S. Shelah: A combinatorial problem,Pacific J. Math. 41 (1972), 247–261.

    Google Scholar 

  3. [3]

    V. N. Vapnik, andA. J. Ĉervonenkis: The uniform convergence of frequencies of the apperance of events to their probabilities, (in Russian),Teor. Veroyatn. Primen.,16 (1971), 267–279.

    Google Scholar 

  4. [4]

    P. Frankl, andJ. Pach: On disjointly representable sets, Combinatorica4 (1984), 39–45.

    Google Scholar 

  5. [5]

    P. Frankl, andM. Watanabe: Density results for uniform families,Combinatorica 14 (1) (1994), 115–119.

    Google Scholar 

  6. [6]

    P. Erdős: On some problems in graph theory, combinatorial analysis and combinatorial number theory, in:Graph theory and combinatorics (Cambridge, 1983), 1–17. B. Bollobás ed., Academic Press, London, 1984.

    Google Scholar 

  7. [7]

    P. Erdős, C. Ko, andR. Rado: Intersection theorems for systems of finite sets,Quart. J. Math. Oxford (2)12 (1961), 313–320.

    Google Scholar 

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Ahlswede, R., Khachatrian, L.H. Counterexample to the Frankl-Pach conjecture for uniform, dense families. Combinatorica 17, 299–301 (1997). https://doi.org/10.1007/BF01200912

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Mathematics Subject Classification (1991)

  • 05D05