[seqfan] Re: Arranging circles on a sphere -- A000055?

[Hugo Pfoertner]

It might be interesting to compare your general case with the special cases
of circle arrangements in
http://oeis.org/A000109 , http://oeis.org/A000103 , http://oeis.org/A007022
, http://oeis.org/A081621

Hugo Pfoertner

On Sat, Aug 13, 2016 at 9:49 PM, Vladimir Reshetnikov <
v.reshetnikov at gmail.com> wrote:

> Dear SeqFans,
>
>
>
> I was thinking on the following problem:
>
>
>
> What is the number of ways to arrange n unlabeled non-intersecting circles
> on a sphere? Two arrangements are considered equivalent iff they can be
> transformed to one another by a combination of the following motions:
> (1) reflection, (2) continuously moving circles, (3) continuously changing
> their radii, provided that the circles always stay non-intersecting and lie
> on the sphere.
>
>
>
> After some thought, it occurred to me that there is an isomorphism between
> an arrangement of circles and a tree with unlabeled nodes — the fragments
> of the sphere separated by circles correspond to the nodes of the tree, and
> the circles correspond to the edges. An edge connects two nodes, iff the
> corresponding circle is the common boundary of two fragments.
> Simply-connected fragments ("caps") correspond to the leaf nodes.
>
>
>
> So it seems the sequence I'm looking for is just http://oeis.org/A000055.
> Am I right? Do we get the same result if we exclude reflection from the
> allowed motions?
>
>
>
> --
>
> Thanks
>
> Vladimir Reshetnikov
>
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