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Lower Bound for the Maximal Number of Facets of a 0/1 Polytope |
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| Authors: | Dimitris Gatzouras Giannopoulos Apostolos Nikolaos Markoulakis |
| Affiliation: | (1) Department of Mathematics, Agricultural University of Athens, Iera Odos 75, 118 55 Athens, Greece;(2) Department of Mathematics, University of Athens, Panepistimiopolis, 157 84 Athens, Greece;(3) Department of Mathematics, University of Crete, Heraklion 714 09, Crete, Greece |
| Abstract: | Let $f_{n-1}(P)$ denote the number of facets of apolytope $P$ in ${Bbb R}^n$. We show that there exist 0/1polytopes $P$ with $$f_{n-1}(P)geqleft (frac{cn}{log^2n}right )^{n/2},$$ where $c>0$ is an absolute constant. Thisimproves earlier work of Barany and Por on a questionof Fukuda and Ziegler. |
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