### 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 |
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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 |

### Keywords

- LR number
- LR word
- Spherical closed curve

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Takaoka, K. (2015). LR number of spherical closed curves.

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