[seqfan] Re: How many squares can you make from n points in the plane?
Benoît Jubin
benoit.jubin at gmail.com
Fri Oct 1 00:42:35 CEST 2021
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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