Abstract
We give a new upper bound onn d(d+1)n on the number of realizable order types of simple configurations ofn points inR d, and ofn2d 2 n on the number of realizable combinatorial types of simple configurations. It follows as a corollary of the first result that there are no more thann d(d+1)n combinatorially distinct labeled simplicial polytopes inR d withn vertices, which improves the best previous upper bound ofn cnd/2.
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Communicated by Branko Grünbaum
Supported in part by NSF Grant DMS-8501492 and PSC-CUNY Grant 665258.
Supported in part by NSF Grant DMS-8501947.
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Goodman, J.E., Pollack, R. Upper bounds for configurations and polytopes inR d . Discrete Comput Geom 1, 219–227 (1986). https://doi.org/10.1007/BF02187696
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DOI: https://doi.org/10.1007/BF02187696