Minimal generating set size

[Edwin Clark]

On Tue, 14 Mar 2006, Joshua Zucker wrote:

> On 3/14/06, Edwin Clark <eclark at math.usf.edu> wrote:
> > In addition I computed the following values for the two dimensional
> > case: 4,4,4,6,6,7 for the cases n = 1,2,3,4,5,6 where the n-th
> > square is {(x,y): x,y in {0,1,...,n}}. I plan to add this to the
> > OEIS soon. I want to first look at Guy's book and the Alon paper
> > to see if they have calculated more values.
> >
> > Unless I learn of a better technique, getting exact values for the
> > three dimensional case for small n looks out of reach for now.
> >
> > --Edwin
> 
> Did you get your values by (1) finding a
> set of that many points that works, and (2) exhaustively searching all
> sets of fewer points to show they don't work?  Or is there something
> smarter that I'm missing?
> 

Yes, brute force is pretty much how I did it. Actually the hard part
is exhaustive search to eliminate sets of fewer points. Also I used
Maple. Certainly something like C would be faster. I just printed
out Alon's paper to see how he gets his lower bounds.