On triangulations of the convex hull ofn points


A setS ofn points in Euclideand-space determines a convex hull which can be triangulated into some numberm of simplices using the points ofS as vertices. We characterize those setsS for which all triangulations minimizem. This is used to characterize sets of points maximizing the volume of the smallest non-trivial simplex.

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  1. [1]

    E. O. Buchman andF. A. Valentine, A characterization of convex surfaces which are L-sets,Proc. A.M.S. 40 (1973), 235–239.

    MATH  Article  MathSciNet  Google Scholar 

  2. [2]

    P. Erdős, G. Purdy andE. G. Straus, On a problem in combinatorial geometry,Discrete Math. 40 (1982), 45–52.

    Article  MathSciNet  Google Scholar 

  3. [3]

    J. Komlós, J. Pintz andE. Szemerédi, On Heilbronn’s triangle problem,J. Lond Math. Soc. (2) 24 (1981), 385–396.

    MATH  Article  Google Scholar 

  4. [4]

    J. Komlós, J. Pintz andE. Szemerédi, A lower bound for Heilbronn’s problem,J. Lond. Math. Soc. (2) 25 (1982), 13–24.

    MATH  Article  Google Scholar 

  5. [5]

    R. P. Stanley, The number of faces of simplicial polytopes and spheres,to appear, Proc. N. Y. Acad. Sci.

  6. [6]

    R. P. Stanley, The upper bound conjecture and Cohen-Macauley Rings.Studies in Applied Math. 54 (1975) 135–142.

    MathSciNet  Google Scholar 

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Dedicated to Paul Erdős on his seventieth birthday

This work was supported in part by NSF Grants MCS 81-02519 and MCS 82-03347.

This work supported in part by NSF Grants MCS 81-02519 and MCS 82-03347

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Rotschild, B.L., Straus, E.G. On triangulations of the convex hull ofn points. Combinatorica 5, 167–179 (1985). https://doi.org/10.1007/BF02579380

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AMS subject classification (1980)

  • 51 M 05
  • 52 A 20