[seqfan] Re: partition of a circle

[Neil Sloane]

Wolfdieter, I don't think that rule is needed.
I think the following is a legitimate dissection (into 16 regions):
draw a square grid with 5 horizontal lines and 5 vertical lines.
The boundary is a square, but topologically that is the same as
a circle. There are 12 P's and 9 Q's.
I asked Tudor Z. if he knew the next term, but he said no.
Neil


On Fri, May 11, 2012 at 3:10 AM, <wl at particle.uni-karlsruhe.de> wrote:

> Maybe one should also include the rule:
> There has to be at least one line segment (edge) connecting each internal
> node Q  to a boundary node P. This would exclude Andrews n=3 and n=5
> graphs, and also Andrew's n=5 graph with all of the four 'outer' Qs
> connected to some Ps (now n=8), but the 'central' node Q is not connected
> to any P. Such a  central Q is never connectable to any P  (planarity).
>
> I have written yesterday to one of the authors (T. Zamfirescu at Dortmund
> TH) my zeroth order guess of the rules, and asked him for a definition of
> 'Jordan domain' on a euclidean plane E_2 (maybe some fans can here help
> also). I am waiting for his answer.
>
> Wolfdieter Lang
>
>
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