[seqfan] Re: Sequence re partitions of n-gon needs more terms

[Andrew Weimholt]

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