[seqfan] Self avoiding polygons

[John Mason]

Hi seqfans.
I would be grateful if anyone could tell me of an existing proof of the following assertion, relative to self-avoiding polygons on the square lattice (aka the boundaries of “profane” polyominoes):

Premise: one way to build such a polygon of perimeter 2n+2 is to take a polygon of perimeter 2n, find within that polygon a segment of length s, and “shift” a component of that segment, of integral length, “outwards” by one unit, but only if such a manoeuvre does not touch, even at a corner, any existing part of the polygon.
So for example:
OOO
OOO
OOO
Can generate (among others):
OOO
OOOO
OOOO

Assertion: any self-avoiding polygon on the square lattice, of size 2n+2, for n > 2, may be generated from some polygon of size 2n by using the above-described procedure.

Grateful for your help
john





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