# [seqfan] Re: partition of a circle

Neil Sloane njasloane at gmail.com
Sat May 12 06:06:12 CEST 2012

```PS Also, Ed, we do not allow more than one edge between two nodes. I think
your example violates this rule too.
Neil

On Sat, May 12, 2012 at 12:03 AM, Neil Sloane <njasloane at gmail.com> wrote:

>
> In your example, the left piece and the right piece
> have a common boundary which is not connected,
> and so this is not admissible.
>
> The pieces, as I said, do NOT need to be assumed to be convex.
>
> Neil
>
>
> On Fri, May 11, 2012 at 11:05 PM, Ed Jeffery <lejeffery7 at gmail.com> wrote:
>
>> Neil,
>>
>> Sorry to butt in again, but I think Valette-Z. mean that the pieces have
>> null intersection except at their boundaries, with their disjoint union
>> being the entire disk (circle); i.e., as with tiles, the pieces must fit
>> together without gaps or overlaps.
>>
>> As for convexity, surely the pieces must be convex, since otherwise the
>> example (for n = 3) I sent to you would be a valid candidate. To describe
>> that example again: draw a smaller circle inside the larger circle to be
>> divided, then draw two lines, each extending from the smaller circle to
>> the
>> larger one, and which divide the annulus into two pieces without either
>> line intersecting the interior of the smaller circle or disk. The two
>> pieces forming the annulus can't be convex.
>>
>> Ed
>>
>> > Wolfdieter, Yes, I agree that we need more conditions
>> > that will rule out your example.
>>
>> > In fact in the Valette-Z. paper, they add the condition
>> > that the partition must be admissible, which
>> > they define to mean that if K and L are two distinct pieces,
>> > then the intersection (boundary of K) intersect (boundary of L)
>> > is connected.
>> > This rules out your example, since the two big pieces has intersection
>> > which is not connected.
>>
>> > By the way, they do NOT require that the pieces be convex. (That would
>> be
>> > another way to
>> > rule out your example)
>>
>> > Neil
>>
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>>
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>>
>
>
>
> --
> Dear Friends, I will soon be retiring from AT&T. New coordinates:
>
> Neil J. A. Sloane, President, OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA
> Email: njasloane at gmail.com
>
>
>

--
Dear Friends, I will soon be retiring from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA