### Abstract

Knots and links have been considered to be useful models for structural analysis of molecular chains such as DNA and proteins. One quantity that we are interested in for molecular links is the minimum number of monomers necessary for realizing them. In this paper we consider every link in the cubic lattice. The lattice stick number s<inf>L</inf>(L) of a link L is defined to be the minimum number of sticks required to construct a polygonal representation of the link in the cubic lattice. Huh and Oh found all knots whose lattice stick numbers are at most 14. They proved that only the trefoil knot 3<inf>1</inf> and the figure-eight knot 4<inf>1</inf> have lattice stick numbers of 12 and 14, respectively. In this paper we find all links with more than one component whose lattice stick numbers are at most 14. Indeed we prove combinatorically that , , , and any other non-split links have stick numbers of at least 15.

Original language | English |
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Article number | 155202 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 47 |

Issue number | 15 |

DOIs | |

Publication status | Published - 2014 Apr 18 |

### Fingerprint

### Keywords

- cubic lattice
- knot
- stick number

### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*47*(15), [155202]. https://doi.org/10.1088/1751-8113/47/15/155202

**Links with small lattice stick numbers.** / Hong, Kyungpyo; No, Sungjong; Oh, Seung Sang.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 47, no. 15, 155202. https://doi.org/10.1088/1751-8113/47/15/155202

}

TY - JOUR

T1 - Links with small lattice stick numbers

AU - Hong, Kyungpyo

AU - No, Sungjong

AU - Oh, Seung Sang

PY - 2014/4/18

Y1 - 2014/4/18

N2 - Knots and links have been considered to be useful models for structural analysis of molecular chains such as DNA and proteins. One quantity that we are interested in for molecular links is the minimum number of monomers necessary for realizing them. In this paper we consider every link in the cubic lattice. The lattice stick number sL(L) of a link L is defined to be the minimum number of sticks required to construct a polygonal representation of the link in the cubic lattice. Huh and Oh found all knots whose lattice stick numbers are at most 14. They proved that only the trefoil knot 31 and the figure-eight knot 41 have lattice stick numbers of 12 and 14, respectively. In this paper we find all links with more than one component whose lattice stick numbers are at most 14. Indeed we prove combinatorically that , , , and any other non-split links have stick numbers of at least 15.

AB - Knots and links have been considered to be useful models for structural analysis of molecular chains such as DNA and proteins. One quantity that we are interested in for molecular links is the minimum number of monomers necessary for realizing them. In this paper we consider every link in the cubic lattice. The lattice stick number sL(L) of a link L is defined to be the minimum number of sticks required to construct a polygonal representation of the link in the cubic lattice. Huh and Oh found all knots whose lattice stick numbers are at most 14. They proved that only the trefoil knot 31 and the figure-eight knot 41 have lattice stick numbers of 12 and 14, respectively. In this paper we find all links with more than one component whose lattice stick numbers are at most 14. Indeed we prove combinatorically that , , , and any other non-split links have stick numbers of at least 15.

KW - cubic lattice

KW - knot

KW - stick number

UR - http://www.scopus.com/inward/record.url?scp=84937032443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937032443&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/15/155202

DO - 10.1088/1751-8113/47/15/155202

M3 - Article

AN - SCOPUS:84937032443

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 15

M1 - 155202

ER -