<B>Abstract</B><P>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...
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https://www.riss.kr/link?id=A107463618
2018
-
SCOPUS,SCIE
학술저널
518-530(13쪽)
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
<B>Abstract</B><P>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...
<B>Abstract</B><P>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 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 = 2<SUP>n−1</SUP> − 1. And for integers m, n ≥ 3,</P><P/>
Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians