Geodesic
Asymptotics of polygons in restricted geometries subject to a force
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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We consider self-avoiding polygons in a restricted geometry, namely an infinite L × M tube in Z3. 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. In this extended abstract we obtain and prove the asymptotic form of the free energy in the limit f → −∞. We conjecture that the f → −∞ asymptote is the same as the free energy of Hamiltonian polygons, which visit every vertex in a L × M × N box. 
@article{DMTCS_2020_special_379_a12,
     author = {Beaton, Nicholas and Eng, Jeremy and Soteros, Christine},
     title = {Asymptotics of polygons in restricted geometries subject to a force},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6330},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6330/}
}
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Beaton, Nicholas; Eng, Jeremy; Soteros, Christine. Asymptotics of polygons in restricted geometries subject to a force. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6330. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6330/

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