Bulletin (New Series) of the American Mathematical Society

There are asymptotically far fewer polytopes than we thought

Jacob E. Goodman and Richard Pollack

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.) Volume 14, Number 1 (1986), 127-129.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.bams/1183552790

Mathematical Reviews number (MathSciNet)
MR818067

Zentralblatt MATH identifier
0585.52003

Subjects
Primary: 52A25
Secondary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 14G30 51M20: Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]

Citation

Goodman, Jacob E.; Pollack, Richard. There are asymptotically far fewer polytopes than we thought. Bulletin (New Series) of the American Mathematical Society 14 (1986), no. 1, 127--129. http://projecteuclid.org/euclid.bams/1183552790.


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References

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  • 2. J. E. Goodman and R. Pollack, Multidimensional sorting, SIAM J. Comput. 12 (1983), 484-507.
  • 3. J. E. Goodman and R. Pollack, Upper bounds for configurations and polytopes in Rd, Discrete Comp. Geom. (to appear).
  • 4. B. Grünbaum, Convex polytopes, Interscience-Wiley, London, 1967.
  • 5. V. Klee, The number of vertices of a convex polytope, Canad. J. Math. 16 (1964), 701-720.
  • 6. J. Milnor, On the Betti numbers of real varieties, Proc. Amer. Math. Soc. 15 (1964), 275-280.
  • 7. I. Shemer, Neighborly polytopes, Israel J. Math. 43 (1982), 291-314.