[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
>
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