[seqfan] Re: partitions of a circle

[Andrew Weimholt]

On 5/10/12, Neil Sloane <njasloane at gmail.com> wrote:
>
> I could write out a set of rules, I think. We describe
> the picture by giving a list of points P_1, P_2, ... going around the
> boundary, together with interior points Q_1, Q_2, ...
> Then we just say what the lines are joining the points.
>

The rules need a little more fleshing out...

For example,
1. Every edge must separate two distinct regions.
2. Every interior vertex (Q_1, Q_2, ...) must have valence >= 3

otherwise we could have figures such as the following
[view in a fixed-width font]:

        Q
       / \
  P---Q---Q---P

  (for n=2)

OR      Q
       /|\
  P---Q-Q-Q
       \ /
        Q

  (for n=4)
  Note: the P-Q edge borders the same region on both sides.

Andrew