How many figure eights are there? Some bounds
- 1 June 1977
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 10 (6) , L111-L112
- https://doi.org/10.1088/0305-4470/10/6/003
Abstract
The letter gives a short proof that the number of figure eights weakly embeddable in a lattice is at least comparable to, and may be much larger than, the number of polygons, when the number of edges in the graph is sufficiently large.Keywords
This publication has 4 references indexed in Scilit:
- Limiting ring closure probabilities in the self-avoiding walk problemJournal of Physics A: General Physics, 1975
- Figure eights on the square lattice: enumeration and Monte Carlo estimationJournal of Physics A: General Physics, 1970
- Probability of Initial Ring Closure for Self-Avoiding Walks on the Face-Centered Cubic and Triangular LatticesThe Journal of Chemical Physics, 1967
- The number of polygons on a latticeMathematical Proceedings of the Cambridge Philosophical Society, 1961