# [seqfan] Re: partitions of a circle

Andrew Weimholt andrew.weimholt at gmail.com
Fri May 11 02:00:21 CEST 2012

```correction...
The first figure would be n=3, not n=2

Also, in the second figure, I should've
included another line segment and made it n=5
to illustrate that a "bad" edge can arise even
without any interior points with valence < 3.

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

Andrew

On 5/10/12, Andrew Weimholt <andrew.weimholt at gmail.com> wrote:
> 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
>

```