Knots in self-avoiding walks
- 7 April 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (7) , 1689-1694
- https://doi.org/10.1088/0305-4470/21/7/030
Abstract
Discusses the existence of knots in random self-avoiding walks on a lattice. Using Kesten's (1963) pattern theorem, it is shown that almost all sufficiently long self-avoiding walks on the three-dimensional simple cubic lattice contain a knot.Keywords
This publication has 11 references indexed in Scilit:
- Topological constraints and their influence on the properties of synthetic macromolecular systems. 1. Cyclic macromoleculesMacromolecules, 1987
- Biochemical Topology: Applications to DNA Recombination and ReplicationScience, 1986
- On the topology of a polymer ringProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1986
- Tight knotsMacromolecules, 1984
- Topological constraints on polymer rings and critical indicesJournal de Physique, 1979
- Statistical mechanics with topological constraints: IProceedings of the Physical Society, 1967
- On the Number of Self-Avoiding WalksJournal of Mathematical Physics, 1963
- Mathematical Problems in the Biological SciencesPublished by American Mathematical Society (AMS) ,1962
- Chemical Topology1Journal of the American Chemical Society, 1961
- The number of polygons on a latticeMathematical Proceedings of the Cambridge Philosophical Society, 1961