Minimal generating set size

[Hugo Pfoertner]

Edwin Clark wrote:
> 
> On Tue, 14 Mar 2006, Dan Dima wrote:
> 
> > Here are some links for the 2-dimensional version of the problem:
> >
> > http://mathforum.org/kb/message.jspa?messageID=3545255&tstart=0
> > http://www.mathlinks.ro/Forum/viewtopic.php?t=6159
> >
> > It seems that:
> > a*n^{2/3} <= f(n) <= b*n^{2/3}*log(n).
> >
> 
> With the help of the clue that Noga Alon obtained these bounds from one
> of the postings I found the following abstract of a paper of his which
> has the generalization of the above formula to the d-dimensional case:
> 
> MR1118729 (92g:52017)
> Alon, N.(IL-TLAV)
> Economical coverings of sets of lattice points.
> Geom. Funct. Anal. 1 (1991), no. 3, 224--230.
>

An on-line version of this paper is available from
Noga Alon's publications page
http://www.math.tau.ac.il/~nogaa/PDFS/publications.html
http://www.math.tau.ac.il/~nogaa/PDFS/lattice.pdf

Hugo Pfoertner