[seqfan] Re: Patterson's 1944 triangle

Detlef Pauly dettodet at yahoo.de
Sat Mar 14 12:04:10 CET 2009

The left side of Patterson's Table 1 (possible arrangements) looks like
A052307, A078925.


----- Ursprüngliche Mail ----
Von: N. J. A. Sloane <njas at research.att.com>
An: seqfan at seqfan.eu
CC: math-fun at mailman.xmission.com; njas at research.att.com
Gesendet: Samstag, den 14. März 2009, 07:13:40 Uhr
Betreff: [seqfan]  Patterson's 1944 triangle

Dear SeqFans,

I came across a paper,

Phys. Rev. 65, 195 - 201 (1944)
Ambiguities in the X-Ray Analysis of Crystal Structures
by A L Patterson

http://prola.aps.org/abstract/PR/v65/i5-6/p195_1  is the URL, if
your institution subscribes (mine does not)

In Table I there is a triangle of numbers, which
the author admits he is not confident about (which
is probably why I left them out
of the 1973 book)

I know that there have been several followup papers.

It might be an interesting project for someone to
look into this, determine the correct triangle(s), and submit
it to the OEIS,

The subject is the ways to place n points around a circle so that the 
set of n-choose-2 distances do/do not determine the points

[Related to the classical problem, worked on by Petard, as I recall,
who got it wrong - hoisted with your own Petard? - of when the distances
between n points anywhere in the plane determine the pints.]

Might be an interesting problem to work on (the Patterson paper, I mean).



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