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An Upper-Bound theorem for families of convex sets

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References

  1. Abbott, H. and Katchalski, M., ‘A Turán Type Problem for Interval Graphs’, Discrete Math. 25 (1979), 85–88.

    Google Scholar 

  2. Alon, N. and Kalai, G., ‘A Simple Proof of the Upper Bound Theorem’, European J. Comb. (to appear).

  3. Billera, L. J. and Lee, C. W., ‘A Proof of the Sufficiency of McMullen's Conditions for f-Vectors of Simplicial Convex Polytopes’, J. Comb. Theory Ser. A 31 (1981), 237–255.

    Google Scholar 

  4. Eckhoff, J., ‘Über kombinatorisch-geometrische Eigenschaften von Komplexen und Familien konvexer Mengen’, J. reine angew. Math. 313 (1980), 171–188.

    Google Scholar 

  5. Frankl, P., ‘An Extremal Problem for Two Families of Sets’, European J. Comb. 3 (1982), 125–127.

    Google Scholar 

  6. Kalai, G., ‘Intersection Patterns of Convex Sets’, Israel J. Math. 48 (1984), 161–174.

    Google Scholar 

  7. Kalai, G., ‘Characterization of f-Vectors of Families of Convex Sets in R d. Part I: Necessity of Eckhoff's Conditions’, Israel J. Math. 48 (1984), 175–195.

    Google Scholar 

  8. Kalai, G., ‘Characterization of f-Vectors of Families of Convex Sets in R d. Part II: Sufficiency of Eckhoff's Conditions’, J. Comb. Theory Ser. A (to appear).

  9. McMullen, P., ‘The Maximum Numbers of Faces of a Convex Polytope’, Mathematika 17 (1970), 179–184.

    Google Scholar 

  10. McMullen, P., ‘The Numbers of Faces of Simplicial Polytopes’, Israel J. Math. 9 (1971), 559–570.

    Google Scholar 

  11. Stanley, R. P., ‘The Number of Faces of a Simplicial Convex Polytope’, Adv. in Math. 35 (1980), 236–238.

    Google Scholar 

  12. Wegner, G., ‘Eigenschaften der Nerven homologisch-einfacher Familien im R n’, Dissertation, Göttingen, 1967.

    Google Scholar 

  13. Wegner, G., ‘d-Collapsing and Nerves of Families of Convex Sets’, Arch. Math. 26 (1975), 317–321.

    Google Scholar 

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Eckhoff, J. An Upper-Bound theorem for families of convex sets. Geom Dedicata 19, 217–227 (1985). https://doi.org/10.1007/BF00181472

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  • DOI: https://doi.org/10.1007/BF00181472

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