Polygons in restricted geometries subjected to infinite forces

We consider self-avoiding polygons in a restricted geometry, namely an infinite L x M tube in Z(3). These polygons are subjected to a force f, parallel to the infinite axis of the tube. When f > 0 the force stretches the polygons, while when f < 0 the force is compressive. We obtain and prove the asymptotic form of the free energy in both limits f We conjectucture that the f asymptote is the same as the limiting free energy of 'Hamiltonian' polygons, polygons which visit every vertex in a L x M x N box. We investigate such polygons, and in particular use a transfer-matrix methodology to establish that the conjecture is true for some small tube sizes.