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- W3102350663 abstract "As a discrete counterpart to the classical John theorem on the approximation of (symmetric) $n$-dimensional convex bodies $K$ by ellipsoids, Tao and Vu introduced so called generalized arithmetic progressions $P(A,b)subset Z^n$ in order to cover (many of) the lattice points inside a convex body by a simple geometric structure. Among others, they proved that there exists a generalized arithmetic progressions $P(A,b)$ such that $P(A,b)subset Kcap Z^nsubset P(A,O(n)^{3n/2}b)$. Here we show that this bound can be lowered to $n^{O(ln n)}$ and study some general properties of so called unimodular generalized arithmetic progressions." @default.
- W3102350663 created "2020-11-23" @default.
- W3102350663 creator A5040119486 @default.
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- W3102350663 date "2019-10-11" @default.
- W3102350663 modified "2023-10-04" @default.
- W3102350663 title "Discrete analogues of John’s theorem" @default.
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- W3102350663 doi "https://doi.org/10.2140/moscow.2019.8.367" @default.
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