New Non-Linear Inequalities for Flag-Vectors of 4-Polytopes |
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Authors: | Joseph M. Ling |
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Affiliation: | (1) Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, T2N 1N4, Canada |
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Abstract: | In this paper we prove four new (infinite) lists of quadratic inequalities, and four cubic inequalities, for the flag f-vectors of 4-polytopes. These extend and supplement the only four currently known non-linear inequalities, which were proved by Bayer in 1987. The new lists of inequalities for flag f-vectors yield new lists of inequalities for f-vectors of 4-polytopes. Using the latter, we managed to improve an estimate discovered by Hoppner and Ziegler concerning upper bounds of f1 in terms of f0 and f3. |
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