Bounds on Multiple Self-avoiding Polygons
- Authors
- Hong, Kyungpyo; Oh, Seungsang
- Issue Date
- 9월-2018
- Publisher
- CANADIAN MATHEMATICAL SOC
- Keywords
- ring polymer; self-avoiding polygon
- Citation
- CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, v.61, no.3, pp.518 - 530
- Indexed
- SCIE
SCOPUS
- Journal Title
- CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
- Volume
- 61
- Number
- 3
- Start Page
- 518
- End Page
- 530
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/73167
- DOI
- 10.4153/CMB-2017-072-x
- ISSN
- 0008-4395
- Abstract
- A 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 problem to this study, we consider multiple 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 p(mxn) of distinct multiple self-avoiding polygons in the m x n rectangular grid on the square lattice. For m = 2, p(2xn) = 2(n-1) - 1. And for integers m, n >= 3, 2(m+n-3) (17/10)((m -2) (n-2)) <= p(mxn) <= 2(m+n-3) (13/16)((m-2) (n-2)).
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