Bounds on Multiple Self-avoiding Polygons
2018 ◽
Vol 61
(3)
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pp. 518-530
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Keyword(s):
AbstractA self-avoiding polygon is a lattice polygon consisting of a closed self-avoiding walk on a square lattice. Surprisingly little is known rigorously about the enumeration of self-avoiding polygons, although there are numerous conjectures that are believed to be true and strongly supported by numerical simulations. As an analogous problemto this study, we considermultiple self-avoiding polygons in a confined region as a model for multiple ring polymers in physics. We find rigorous lower and upper bounds for the number pm×n of distinct multiple self-avoiding polygons in the m × n rectangular grid on the square lattice. For m = 2, p2×n = 2n−1 − 1. And for integers m, n ≥ 3,
2002 ◽
Vol 11
(5)
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pp. 433-445
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Keyword(s):