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A Multidimensional critical factorization theorem
No full textThe 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 andWilf, that has several classical generalizations
to the multidimensional case
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