This is an announcement for the paper "Simultaneous packing and covering in sequence spaces" by Konrad J. Swanepoel.

Abstract: We adapt a construction of Klee (1981) to find a packing of unit balls in $\ell_p$ ($1\leq p<\infty$) which is efficient in the sense that enlarging the radius of each ball to any $R>2^{1-1/p}$ covers the whole space. We show that the value $2^{1-1/p}$ is optimal.

Archive classification: math.MG math.FA

Mathematics Subject Classification: 46B20 (primary), 52C17 (secondary)

Remarks: 5 pages

The source file(s), klee.tex: 14156 bytes, is(are) stored in gzipped form as 0806.4473.gz with size 5kb. The corresponding postcript file has gzipped size 92kb.

Submitted from: konrad.swanepoel@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0806.4473

or

http://arXiv.org/abs/0806.4473

or by email in unzipped form by transmitting an empty message with subject line

uget 0806.4473

or in gzipped form by using subject line

get 0806.4473

to: math@arXiv.org.