### 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 Jun 16 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*43*(26), [265002]. https://doi.org/10.1088/1751-8113/43/26/265002

**Knots with small lattice stick numbers.** / Huh, Youngsik; Oh, Seung Sang.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 43, no. 26, 265002. https://doi.org/10.1088/1751-8113/43/26/265002

}

TY - JOUR

T1 - Knots with small lattice stick numbers

AU - Huh, Youngsik

AU - Oh, Seung Sang

PY - 2010/6/16

Y1 - 2010/6/16

N2 - 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 31 and in figure 8 knot 41 are the only knot types of lattice stick number less than 15, which verifies the result from previous numerical estimations on this quantity.

AB - 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 31 and in figure 8 knot 41 are the only knot types of lattice stick number less than 15, which verifies the result from previous numerical estimations on this quantity.

UR - http://www.scopus.com/inward/record.url?scp=77953352939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953352939&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/43/26/265002

DO - 10.1088/1751-8113/43/26/265002

M3 - Article

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 26

M1 - 265002

ER -