### Abstract

The lattice stick number of a knot type is defined to be the minimal number of straight line segments required to construct a polygon presentation of the knot type in the cubic lattice. In this paper, we mathematically prove that the trefoil knot 3_{1} and in figure 8 knot 4_{1} are the only knot types of lattice stick number less than 15, which verifies the result from previous numerical estimations on this quantity.

Original language | English |
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Article number | 265002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

Issue number | 26 |

DOIs | |

Publication status | Published - 2010 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

Huh, Y., & Oh, S. (2010). Knots with small lattice stick numbers.

*Journal of Physics A: Mathematical and Theoretical*,*43*(26), [265002]. https://doi.org/10.1088/1751-8113/43/26/265002