[seqfan] Re: Maximal number of touching points between unit spheres (fwd)

rkg rkg at ucalgary.ca
Mon Mar 12 21:25:49 CET 2018

Dear Karoly,
             Perhaps you can answer this?   R.

---------- Forwarded message ----------
Date: Mon, 12 Mar 2018 13:44:58 +0000
From: Richard J. Mathar <mathar at mpia-hd.mpg.de>
Reply-To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
To: seqfan at seqfan.eu
Subject: [seqfan] Re: Maximal number of touching points between unit spheres

Related to http://list.seqfan.eu/pipermail/seqfan/2018-February/018394.html

My explicit computation for clusters of spheres centered on the f.c.c.
lattice gives 0,1,3,6,8,12,15,... for A214813: a discrepancy at
a(5). [I checked that my number of configurations equals A038173.]

There is a sentence in Bezdeks "Contact numbers..." Disc. Comput. Geom (2012)
saying "if this were true,... if would follow that C_fcc(5)=9", which
might be the reason why currently a(5)=9.

So the question is: 
is A214813(5)=9 correct, perhaps referring to unconstrained/disordered sphere
packings, or do we need to change either the definition or the numbers, or is my
analysis just wrong and missing configurations with 5 spheres on the f.c.c.
lattice? Can anyone provide the sphere center coordinates of 5 spheres
in a f.c.c. lattice with 9 contacts, as claimed in A214813?


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