[seqfan] Re: partitions of a circle
njasloane at gmail.com
Thu May 10 01:38:03 CEST 2012
PS No progress by anyone on the question (number
of ways to partition a circle into n parts), so I will
mention that the V-Z paper is available from Tudor Zamfirescu's home page,
http://tzamfirescu.tricube.de/, see item 62.
The fifteen ways of partitioning a circle into 4 parts
are shown on the second page.
What is the next term?
On Mon, May 7, 2012 at 11:57 PM, Neil Sloane <njasloane at gmail.com> wrote:
> Dear Sequence Fans, There is a paper:
> *Valette, G.*; *Zamfirescu, T.* Les partages d'un polygone convexe en 4 polygones
> semblables au premier. (French) *J. Combinatorial Theory Ser. B* *16 *(1974),
> 1--16. MR0331217 <http://www.ams.org/mathscinet-getitem?mr=0331217> *(48
> *see **http://www.sciencedirect.com/science/journal/00958956/16/1,*
> *which studies the ways to divide a polygon into 4 congruent pieces.
> But they begin by looking at a simpler question:
> the number of ways to divide a circle into 4 pieces: there are 15 ways,
> according to their rules. Similarly, I think there are 4 ways to divide a
> circle into 3 pieces.
> So there is a sequence 1, 1, 4, 15, ... I can't tell yet if it is in the
> OEIS. I scanned in their
> illustration of the 15 partitions into 4 pieces, and I will be happy to
> send it to anyone
> who wants to try to help find the next couple of terms.
> The 4 ways to cut a circle into 3 pieces are:
> 1. draw 2 parallel chords in a circle
> 2. draw a T in a circle
> 3. draw a Y in a circle
> 4. draw a V in a circle
> 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
> Phone: 732 828 6098; home page: http://NeilSloane.com
> 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
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com
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