Journal of Statistical Physics

, Volume 74, Issue 5, pp 1247–1254

The number of smallest knots on the cubic lattice

  • Yuanan Diao
Short Communications

DOI: 10.1007/BF02188227

Cite this article as:
Diao, Y. J Stat Phys (1994) 74: 1247. doi:10.1007/BF02188227


It has been shown that the smallest knots on the cubic lattice are all trefoils of length 24. In this paper, we show that the number of such unrooted knots on the cubic lattice is 3496.

Key Words

Knotsknotted polygonscubic latticeself-avoiding walks

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Yuanan Diao
    • 1
  1. 1.Department of MathematicsKennesaw State CollegeMarietta