Counting n-gons

[Jonathan Post]

This problem does not come up for triangles, but for n-gons with n>3 one can
either restrict to convex n-gons, or allow convex n-gons, such as bowties
and pentagrams.  In the former case, there is a triangle inequality
applicable, which is not the case for convex n-gons.  I am not clear if this
has been addressed.  Also, are not compounds degenerate cases of
star-polygons? Also, are there not various ways to derive equivalence
classes, considering the polygons "the same" under some set of rotations,
reflections? Then, do we want to retrict to "primitive" n-gons, which are
not similar to earlier ones in the list?

On 10/23/06, franktaw at netscape.net <franktaw at netscape.net> wrote:
>
> There's a problem with this formulation.  Triangles are determined up
> to congruence by their side lenths, but polygons with more sides are
> not.  (Consider rhombus vs. square.)
>
> To make it work, you have to define it purely in terms of edge lengths:
> sequences of n positive integers, totalling p, whose largest value is
> less than the sum of the others (equivalently, less than p/2); up to
> equivalence under rotation and reflection.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: davidwwilson at comcast.net
>
> Let f(n,p) be the number of non-congruent integer-sidedn-gons with
> perimeter p. Then f(3,p)= A005044.
>
> Can we come up with a general formula/recurrence for f(n, p)?
>
>
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