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The number of smallest knots on the cubic lattice

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Abstract

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.

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References

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Communicated by H. Kesten

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Diao, Y. The number of smallest knots on the cubic lattice. J Stat Phys 74, 1247–1254 (1994). https://doi.org/10.1007/BF02188227

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Key Words

  • Knots
  • knotted polygons
  • cubic lattice
  • self-avoiding walks