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Sperner families satisfying additional conditions and their convex hulls

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Abstract

The profile of a hypergraph onn vertices is (f 0,...,f n ) wheref i denotes the number ofi-element edges. The extreme points of the set of the profiles are determined for Sperner hypergraphs satisfying some additional conditions. The results contain some old theorems of extremal set theory as particular cases.

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References

  1. Bollobás, B.: Sperner systems consisting of pairs of complementary subsets. J. Comb. Theory (A)15, 363–366 (1973)

    Google Scholar 

  2. Brace, A., Daykin, D.E.: Sperner type theorems for finite sets. In: Combinatorics (Proc. Conf. Combinatorial Math. Oxford, 1972), pp. 18–37. Southend-on-Sea: Inst. Math. Appl. 1972

    Google Scholar 

  3. Clements, G.F., Gronau H.-D.O.F., On maximal antichains containing no set and its complement. Discrete Math.33, 239–247 (1981)

    Google Scholar 

  4. Erdös, P.L., Frankl, P., Katona, G.O.H.: Intersecting Sperner families and their convex hulls. Combinatorica4, 21–34 (1984)

    Google Scholar 

  5. Erdös, P.L., Frankl, P., Katona, G.O.H.: Extremal hypergraph problems and convex hulls. Combinatorica5, 11–26 (1985)

    Google Scholar 

  6. Engel, K., Gronau, H.-D.O.F.: Sperner theory in partially ordered sets. Leipzig: Teubner Verlagsgesellschaft, 1985

    Google Scholar 

  7. Greene, H., Hilton, A.J.W.: Some results on Sperner families. J. Comb. Theory (A)26, 202–209 (1979)

    Google Scholar 

  8. Katona, G.O.H.: Two applications (for search theory and truth functions) of Sperner type theorems. Period. Math. Hung.3, 19–26 (1973)

    Google Scholar 

  9. Kleitman, D., Spencer, J.: Families ofk-independent sets. Discrete Math.6, 255–262 (1973)

    Google Scholar 

  10. Marczewski, E.: Independence d'ensembles et prolongement de mesure. Colloq. Math.1, 122–132 (1984)

    Google Scholar 

  11. Purdy, G.: A result on Sperner collections. Util. Math.13, 95–99 (1977)

    Google Scholar 

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Authors and Affiliations

  1. Section Mathematik, Wilhelm-Pieck-Universität, 2500, Rostock, German Democratic Republic

    Konrad Engel

  2. Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary

    Péter L. Erdös

Authors
  1. Konrad Engel
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  2. Péter L. Erdös
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Engel, K., Erdös, P.L. Sperner families satisfying additional conditions and their convex hulls. Graphs and Combinatorics 5, 47–56 (1989). https://doi.org/10.1007/BF01788657

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