Knots with small lattice stick numbers

Youngsik Huh; Seungsang Oh

doi:10.1088/1751-8113/43/26/265002

Knots with small lattice stick numbers

Youngsik Huh, Seungsang Oh

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

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 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.

Original language	English
Article number	265002
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	43
Issue number	26
DOIs	https://doi.org/10.1088/1751-8113/43/26/265002
Publication status	Published - 2010

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8113/43/26/265002

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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 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.",

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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.

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JO - Journal of Physics A: Mathematical and Theoretical

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Knots with small lattice stick numbers

Abstract

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