### Abstract

The Critical Factorization Theorem is one of the principal results in combinatorics on words. It relates local periodicities of a word to its global periodicity. In this paper we give a multidimensional extension of it. More precisely, we give a new proof of the Critical Factorization Theorem, but in a weak form, where the weakness is due to the fact that we loose the tightness of the local repetition order. In exchange, we gain the possibility of extending our proof to the multidimensional case. Indeed, this new proof makes use of the Theorem of Fine and Wilf, that has several classical generalizations to the multidimensional case

Original language | English |
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Pages (from-to) | 265-280 |

Number of pages | 16 |

Journal | Theoretical Computer Science |

Volume | 346 |

Publication status | Published - 2005 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Mignosi, F., & Epifanio, C. (2005). A Multidimensional Critical Factorization Theorem.

*Theoretical Computer Science*,*346*, 265-280.