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 | References | Similar Articles | Additional Information
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.
- [1] Branko Grünbaum, Convex polytopes, With the cooperation of Victor Klee, M. A. Perles and G. C. Shephard. Pure and Applied Mathematics, Vol. 16, Interscience Publishers John Wiley & Sons, Inc., New York, 1967. MR 0226496
- [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 0247570, https://doi.org/10.1090/S0002-9939-1969-0247570-7
- [4] Joseph Zaks, On a conjecture of A. J. Hoffman, Proc. Amer. Math. Soc. 27 (1971), 122–125. MR 0275282, https://doi.org/10.1090/S0002-9939-1971-0275282-1
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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
