[seqfan] Re: How many squares can you make from n points in the plane?

[Neil Sloane]

Benoit,  There have been so many new developments (they are all in this
email thread, though), that I have lost track of where we are.

But you seem to be on top of things.  Could I ask you to edit the entry,
and bring it up to date?

I'll send you the text file of the a(7) = 3 proof, in case it will be
useful.

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Thu, Sep 30, 2021 at 6:42 PM Benoît Jubin <benoit.jubin at gmail.com> wrote:

> On Thu, Sep 30, 2021 at 10:01 PM Frank Adams-watters via SeqFan
> <seqfan at list.seqfan.eu> wrote:
> >
> > Does this actually get us any new values? I.e., min = max.
>
> Apparently it does not.  So far, we have exact values (for both a(n)
> and b(n)) for n up to 9, thanks to Sascha.
>
> Peter's configurations are clever.  They made me think of two things:
>
> * An interesting representation of a configuration is an integer
> matrix where integers represent the number of squares a given vertex
> belongs to. For instance:
> optimal 6-configurations:
> 121
> 121
> and
> 010
> 211
> 120
> optimal 9-configuration:
> 232
> 343
> 232
> etc.
>
> * The "asymptotic solution" is not the full [1,sqrt(n)]^2 grid but may
> be the full disc of radius sqrt(n/pi).
>
> Benoît
>
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