Discrete & Computational Geometry

, Volume 6, Issue 3, pp 287–289 | Cite as

A simple and relatively efficient triangulation of then-cube

  • Mark Haiman
Article

Abstract

The only previously published triangulation of then-cube usingo(n!) simplices, due to Sallee, usesO(n−2n!) simplices. We point out a very simple method of achievingO(ρnn!) simplices, where ρ<1 is a constant.

Keywords

Discrete Math Discrete Comput Geom Regular Polytopes Minimal Triangulation Stanley Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    L. J. Billera, R. Cushman, and J. A. Sanders, The Stanley decomposition of the harmonic oscillator,Nederl. Akad. Wetensch. Proc. Ser. A 91 (1988), 375–393.MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. W. Cottle, Minimal triangulations of the 4-cube,Discrete Math. 40 (1982), 25–29.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    C. Lee, Triangulating thed-cube, inDiscrete Geometry and Convexity, J. E. Goodman, E. Lutwak, J. Malkevitch, and R. Pollack, eds., New York Academy of Sciences, New York (1985), pp. 205–211.Google Scholar
  4. 4.
    C. Lee, Some notes on triangulating polytopes, inProc. 3. Kolloquium über Diskrete Geometrie, Institut für Mathematik, Universität Salzburg (1985), pp. 173–181.Google Scholar
  5. 5.
    P. S. Mara, Triangulations of the Cube, M, S. Thesis, Colorado State University (1972).Google Scholar
  6. 6.
    J. F. Sallee, A triangulation of then-cube,Discrete Math. 40 (1982), 81–86.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    J. F. Sallee, Middle-cut triangulations of then-cube,SIAM J. Algebraic Discrete Methods 5, no. 3 (1984), 407–419.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    W. D. Smith, Polytope triangulations ind-space, improving Hadamard's inequality and maximal volumes of regular polytopes in hyperbolicd-space. Manuscript, Princeton, NJ (September 1987).Google Scholar
  9. 9.
    R. P. Stanley, Decompositions of rational convex polytopes,Ann. Discrete Math. 6 (1980), 333–342.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    R. P. Stanley,Enumerative Combinatorics, Vol. I, Wadsworth & Brooks/Cole, Monterey, CA (1986).CrossRefMATHGoogle Scholar
  11. 11.
    M. J. Todd,The Computation of Fixed Points and Applications, Lecture Notes in Economics and Mathematical Systems, Vol. 124, Springer-Verlag, Berlin (1976).MATHGoogle Scholar
  12. 12.
    B. Von Hohenbalken, How To Simplicially Partition a Polytope, Research Paper No. 79-17, Department of Economics, University of Alberta, Edmonton (1979).Google Scholar

Copyright information

© Springer-Verlag New York Inc 1991

Authors and Affiliations

  • Mark Haiman
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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