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

hv at crypt.org hv at crypt.org
Thu Oct 7 13:01:02 CEST 2021

Earlier I wrote:
:I've [...] confirmed that the
:figures Sean derived using the "exhaustive search for grid points
:within a square of side ceil(sqrt(n))" are identical to those derived
:by "exhaustive search of all 1- and 2-points extensions starting from
:a unit square".
:Are we ready to conjecture that all maximal arrangements can be
:generated by such extensions? If we are, it's worth noting that this
:also trivially implies a(n) = b(n).

Sascha Kurz has sent me some examples that refute this conjecture:
these 8-point. 3-square arrangements cannot be generated using my
iterative 1- or 2-point extension approach:

xxx.   .xx.   xxx.
.x.x   x.x.   xx.x
x.x.   .x.x   x.x.
..x.   .xx.


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