McMullen's conditions and some lower bounds for general convex polytopes |
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| Authors: | Antoine Deza Komei Fukuda |
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| Institution: | (1) Department of Information Sciences, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro-ku, 152 Tokyo, Japan;(2) centre d'Orsay, Université de Paris-sud, LRI, bât. 490, 91405 Paris Cedex, France;(3) Graduate School of Systems Management, University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, 112 Tokyo, Japan |
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| Abstract: | We give a lower bound for the number of vertices of a generald-dimensional polytope with a given numberm ofi-faces for eachi = 0,...,  d/2 – 1. The tightness of those bounds is proved using McMullen's conditions. Form greater than a small constant, those lower bounds are attained by simpliciali-neighbourly polytopes. |
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| Keywords: | 52B05 52B11 |
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