On the Complexity of the Set of Unconditional Convex Bodies.
| Autor: | Rudelson, Mark |
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| Předmět: | |
| Zdroj: | Discrete & Computational Geometry; Jan2016, Vol. 55 Issue 1, p185-202, 18p |
| Abstrakt: | We show that for any $$1 \le t \le \tilde{c} n^{1/2} \log ^{-5/2} n$$ , the set of unconditional convex bodies in $$\mathbb {R}^n$$ contains a t-separated subset of cardinality at least This implies the existence of an unconditional convex body in $$\mathbb {R}^n$$ which cannot be approximated within the distance d by a projection of a polytope with N faces unless $$N \ge \exp (c(d) n)$$ . We also show that for $$t \ge 2$$ , the cardinality of a t-separated set of completely symmetric bodies in $$\mathbb {R}^n$$ does not exceed . [ABSTRACT FROM AUTHOR] |
| Databáze: | Complementary Index |
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