### Abstract

Given a set Vn={v1,…,vn} of n symbols, a sequence x= x1x2…xm is called a weak Langford string if xi∊ Vnfor 1≤i≤m, and any two consecutive occurrences of vjin x are separated by precisely j characters of x, 1≤i≤m. Proving subsequent conjectures of Păun [5] and Marcus and Păun [4], we show that every weak Langford string is square-free. As a consequence, all Langford languages are finite. Some related questions are raised.

Original language | English |
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Pages (from-to) | 75-78 |

Number of pages | 4 |

Journal | International Journal of Computer Mathematics |

Volume | 29 |

Issue number | 2-4 |

DOIs | |

Publication status | Published - 1989 |

### Fingerprint

### Keywords

- finite language
- Langford string
- Square-free language

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Applied Mathematics

### Cite this

**Langford strings are square-free.** / Tuza, Z.

Research output: Contribution to journal › Article

*International Journal of Computer Mathematics*, vol. 29, no. 2-4, pp. 75-78. https://doi.org/10.1080/00207168908803750

}

TY - JOUR

T1 - Langford strings are square-free

AU - Tuza, Z.

PY - 1989

Y1 - 1989

N2 - Given a set Vn={v1,…,vn} of n symbols, a sequence x= x1x2…xm is called a weak Langford string if xi∊ Vnfor 1≤i≤m, and any two consecutive occurrences of vjin x are separated by precisely j characters of x, 1≤i≤m. Proving subsequent conjectures of Păun [5] and Marcus and Păun [4], we show that every weak Langford string is square-free. As a consequence, all Langford languages are finite. Some related questions are raised.

AB - Given a set Vn={v1,…,vn} of n symbols, a sequence x= x1x2…xm is called a weak Langford string if xi∊ Vnfor 1≤i≤m, and any two consecutive occurrences of vjin x are separated by precisely j characters of x, 1≤i≤m. Proving subsequent conjectures of Păun [5] and Marcus and Păun [4], we show that every weak Langford string is square-free. As a consequence, all Langford languages are finite. Some related questions are raised.

KW - finite language

KW - Langford string

KW - Square-free language

UR - http://www.scopus.com/inward/record.url?scp=84948267471&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948267471&partnerID=8YFLogxK

U2 - 10.1080/00207168908803750

DO - 10.1080/00207168908803750

M3 - Article

AN - SCOPUS:84948267471

VL - 29

SP - 75

EP - 78

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

SN - 0020-7160

IS - 2-4

ER -