[seqfan] Re: partitions of a circle

[Neil Sloane]

Ed:

What you describe is topologically the same as No. 3 on the lst.

(Take the PI, now raise the both arms
until they point straight upwards -
In other words draw an H inside a circle.)

The rules seem to be that you cannot change incidences
or meeting points, and lines can't cross. But kinks and bends
don't matter.

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.

On Thu, May 10, 2012 at 2:02 PM, Ed Jeffery said:
>
>
> Trying to work through n = 5 using a CAD program, the rules are not clear
> to me either. For n = 4, one can draw a lower-case Greek letter "pi" using
> straight line segments extended to meet the circle. This version is not in
> the list of figures, so it must have been taken by the authors to be
> homeomorphic to at least one of the fifteen figures shown, but which
> one(s)? This leads me to wonder, with great frustration: what is the
> distinction between figures 5, 6, 9, 10, 11, 12, 13 and 15 (although it is
> easy to see that they can be represented by distinct graphs)? Finally, it
> seems that nontrivial reflections should be allowed (in the sense that a
> derived figure cannot otherwise be obtained simply by rotation of the
> original), in which case at least one possibility seems to be missing from
> the list for n = 4.
>
> Ed
>
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