Re: question on fitting a function to an actual distribution

[American Citizen <website.reader3@gmail.com>]

Bill

fascinating paper, thanks for the post. I actually previously did some 
of the S2 distributions myself, and plotted them, and it makes me happy 
to see that the author also did this in this paper.

Randall

On 11/27/25 05:23, Bill Allombert wrote:
> On Wed, Nov 26, 2025 at 04:53:30PM -0800, American Citizen wrote:
> > Hello:
> >
> > I have been pushing forward, using a function in gp-pari script written by
> > Max Alekseyev, which finds how many sets of square triads might sum to a
> > given number. For example n=194 results in [[0, 5, 13], [1, 7, 12], [3, 4,
> > 13], [3, 8, 11], [5, 5, 12], [7, 8, 9]] or six triads, the number 194 is the
> > smallest for 6 triads. His program works very well, and I verified it for
> > the values of 1 <= n <= 1e7. (first 240 values of rel max highs)
> >
> > I have a collection of 41,374 triad counts for the 1 <= count <= 41374 with
> > the n value given.
> >
> > This distribution seems to follow:
> >
> > (1)  n =  5.32459104391076 * count ^ 1.93934231682073
> >
> > which is a linear graphic when plotted on a log-log scale.
> I think using the theta function definition of the number of triple lead
> to a much more natural formula.
> See https://www.cirm-math.fr/RepOrga/2062/Slides/Humphries.pdf
>
> Cheers,
> Bill