### Abstract

For a given oriented spherical closed curve with n transversal double points, we assign a cyclic word of length 2n on two letters L standing left and R standing right by reading the crossing sign so that each crossing point is read once L and once R. The LR number of the curve is the number of appearance of subwords LR in the cyclic word. We completely determine oriented spherical closed curves whose LR numbers are less than or equal to three.

Original language | English |
---|---|

Pages (from-to) | 491-503 |

Number of pages | 13 |

Journal | Tokyo Journal of Mathematics |

Volume | 38 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2015 Dec 1 |

### Fingerprint

### Keywords

- LR number
- LR word
- Spherical closed curve

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Tokyo Journal of Mathematics*,

*38*(2), 491-503. https://doi.org/10.3836/tjm/1452806052

**LR number of spherical closed curves.** / Takaoka, Kuniyuki.

Research output: Contribution to journal › Article

*Tokyo Journal of Mathematics*, vol. 38, no. 2, pp. 491-503. https://doi.org/10.3836/tjm/1452806052

}

TY - JOUR

T1 - LR number of spherical closed curves

AU - Takaoka, Kuniyuki

PY - 2015/12/1

Y1 - 2015/12/1

N2 - For a given oriented spherical closed curve with n transversal double points, we assign a cyclic word of length 2n on two letters L standing left and R standing right by reading the crossing sign so that each crossing point is read once L and once R. The LR number of the curve is the number of appearance of subwords LR in the cyclic word. We completely determine oriented spherical closed curves whose LR numbers are less than or equal to three.

AB - For a given oriented spherical closed curve with n transversal double points, we assign a cyclic word of length 2n on two letters L standing left and R standing right by reading the crossing sign so that each crossing point is read once L and once R. The LR number of the curve is the number of appearance of subwords LR in the cyclic word. We completely determine oriented spherical closed curves whose LR numbers are less than or equal to three.

KW - LR number

KW - LR word

KW - Spherical closed curve

UR - http://www.scopus.com/inward/record.url?scp=84981333290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84981333290&partnerID=8YFLogxK

U2 - 10.3836/tjm/1452806052

DO - 10.3836/tjm/1452806052

M3 - Article

AN - SCOPUS:84981333290

VL - 38

SP - 491

EP - 503

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 2

ER -