Abstract of a paper by Konrad J. Swanepoel
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.
participants (1)
-
alspach@fourier.math.okstate.edu