Journal of the ACM (JACM)
Alphabet independent two dimensional matching
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Two-dimensional periodicity and its applications
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
An Alphabet Independent Approach to Two-Dimensional Pattern Matching
SIAM Journal on Computing
Alphabet-Independent Two-Dimensional Witness Computation
SIAM Journal on Computing
Handbook of formal languages, vol. 1
Rotations of periodic strings and short superstrings
Journal of Algorithms
Two-Dimensional Periodicity in Rectangular Arrays
SIAM Journal on Computing
Local periods and propagation of periods in a word
Theoretical Computer Science - Special issue: papers dedicated to the memory of Marcel-Paul Schützenberger
Periodicity and the golden ratio
Theoretical Computer Science - Special issue: papers dedicated to the memory of Marcel-Paul Schützenberger
On Fine and Wilf's theorem for bidimensional words
Theoretical Computer Science
A Unifying Look at d-Dimensional Periodicities and Space Coverings
CPM '93 Proceedings of the 4th Annual Symposium on Combinatorial Pattern Matching
Generalizations of the Periodicity Theorem of Fine and Wilf
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
The definable criterion for definability in Presburger arithmetic and its applications
Theoretical Computer Science
On a conjecture on bidimensional words
Theoretical Computer Science
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Aperiodic Linearly Repetitive Delone Sets Are Densely Repetitive
Discrete & Computational Geometry
Periodicity and local complexity
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
On periodicity of generalized two-dimensional infinite words
Information and Computation
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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.