Coverings and compressed Lattices

by Henk, M.; Hernández Cifre, M. A.


Preprint series: 09-39, Preprints

The paper is published: to appear in special issue on tesselations of \'\'symmetry: culture and science\'\'

52C07 Lattices and convex bodies in $n$ dimensions, See Also {11H06, 11H31, 11P21}
11H06 Lattices and convex bodies, See also {11P21, 52C05, 52C07}


Abstract: Motivated by ``finite alphabet'' approximation problems in infinite-dimensional Banach spaces we study the behavior of the inhomogeneous minimum of a convex body $K$ with respect to the integral lattice $Z^n$, if $Z^n$ is compressed along (some of) the coordinate axes. In particular, we show that for certain convex bodies and deformations the inhomogeneous minimum can be arbitrarily large which answers a question in the negative posted in the context with the above mentioned approximation problems.

Keywords: Coverings, Lattices, Convex bodies

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Letzte Änderung: 01.03.2018 - Ansprechpartner:

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