Counting Self-intersecting n-gons

[David Wilson]

Thank you, I checked out the OEIS sequences related to the reference.

It seems that Welch and Golomb were interested in counting
self-intersecting polygons with vertices equally spaced on a circle.
I am interested in counting self-intersecting polygons without this
restriction.

The problems are not the same, as there are self-intersecting polygons
which cannot be realized with vertices on a circle.  For example,
start with a pentagram and move one vertex to the center of the
pentagram.  The resulting self-intersecting pentagon is not isomorphic
to any of the polygons treated by Welch & Golomb.

----- Original Message ----- 
From: "N. J. A. Sloane" <njas at research.att.com>
To: <ham>; "Sequence Fans" <seqfan at ext.jussieu.fr>; "David Wilson" 
<davidwwilson at comcast.net>
Sent: Friday, April 22, 2005 10:42 AM
Subject: Re: Counting Self-intersecting n-gons


> There is a paper in the Amer. Math. Monthly about this, 30 to 40
> years ago.  The sequences in it are in the OEIS.  The authors were
> some of the usual suspects.
>
> ah yes, here it is:
>
> MR0123487 (23 #A812)
> Golomb, S. W.; Welch, L. R.
> On the enumeration of polygons.
> Amer. Math. Monthly 67 1960 349--353.
> 05.65
> Review in linked PDF Add citation to clipboard Document Delivery Service 
> Journal Original Article
> References: 0 Reference Citations: 0 Review Citations: 0
> There exist $n!$ polygonal paths joining $n$ equally spaced points on a 
> circle. Two polygonal paths which differ only in starting point or 
> orientation give rise to `identical' polygons. If, besides possible 
> difference in starting point and orientation, tw
>
> Reviewed by Seymour Schuster
>
>