[seqfan] Re: Sequence re partitions of n-gon needs more terms
Andrew Weimholt
andrew.weimholt at gmail.com
Fri Feb 18 09:31:27 CET 2011
On Thu, Feb 17, 2011 at 11:59 PM, David Newman <davidsnewman at gmail.com> wrote:
> Perhaps I haven't understood the problem.
> Is it the case that the entire description of the sequence is "re partitions
> of n-gon?"
>
The title says "n-gon {2n}", which is a contradiction.
It should say "2n-gon", or "2*n sided polygon".
"{2n}" is the Schlafli symbol for the regular 2*n sided polygon.
The partitions are not merely any shape bounded by lines through the vertices,
but instead are "ovals", which is a configuration of one or more rhombi in an
approximately oval shape.
For example, the octagon can be partitioned like this...
*-----*
/ /|\
/ / | \
*-----* * *
| | / \ |
| |/ \|
*-----* *
\ \ /
\ \ /
*-----*
or this...
*-----*
/ / \
/ / \
*-----* *
| | |
| | |
*-----* *
\ \ /
\ \ /
*-----*
or this...
*-----*
/ \
/ \
* *
| |
| |
* *
\ /
\ /
*-----*
Hmmm, I get 3 paritions of {8}, and 2 partitions of {6}.
Maybe I also do not understand the author's intent.
It would help if we had access to the preprint.
Andrew
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