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On a conjecture of A. J. Hoffman. II


Author: Joseph Zaks
Journal: Proc. Amer. Math. Soc. 34 (1972), 215-221
MSC: Primary 52A25
DOI: https://doi.org/10.1090/S0002-9939-1972-0296810-7
MathSciNet review: 0296810
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Abstract: It is proved that certain incidence relations of hyperplanes and closed convex sets in a d-polytope can be preserved while replacing these sets by suitable polytopal subsets.


References [Enhancements On Off] (What's this?)

  • [1] B. Grünbaum, Convex polytopes, Pure and Appl. Math., vol. 16, Wiley, New York, 1967. MR 37 #2085. MR 0226496 (37:2085)
  • [2] W. R. Hare, Jr. and C. R. Smith, On convex subsets of a polytope, Proc. Amer. Math. Soc. (to appear).
  • [3] A. J. Hoffman, On the covering of polyhedra by polyhedra, Proc. Amer. Math. Soc. 23 (1969), 123-126. MR 40 #835. MR 0247570 (40:835)
  • [4] J. Zaks, On a conjecture of A. J. Hoffman, Proc. Amer. Math. Soc. 27 (1971), 122-125. MR 0275282 (43:1039)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0296810-7
Keywords: Convex d-polytope, hyperplane, closed convex set
Article copyright: © Copyright 1972 American Mathematical Society

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