Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)

Extended abstracts listed by author > Beaton Nicholas

Asymptotics of polygons in restricted geometries subject to a force
Nicholas Beaton  1  , Jeremy Eng  1  , Christine Soteros  1  
1 : Department of Mathematics and Statistics, [Regina, Saskatchewan]  -  Website
Department of Mathematics & Statistics College West Building, CW307.14 University of Regina 3737 Wascana Parkway Regina, Saskatchewan S4S 0A2 Canada -  Canada

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. 

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