Defect theorem in the plane
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 41 (2007) no. 4, p. 403-409

We consider the defect theorem in the context of labelled polyominoes, i.e., two-dimensional figures. The classical version of this property states that if a set of n words is not a code then the words can be expressed as a product of at most n-1 words, the smaller set being a code. We survey several two-dimensional extensions exhibiting the boundaries where the theorem fails. In particular, we establish the defect property in the case of three dominoes (n × 1 or 1 × n rectangles).

DOI : https://doi.org/10.1051/ita:2007018
Classification:  68Q70,  68R15
Keywords: defect theorem, codes, polyominoes
@article{ITA_2007__41_4_403_0,
     author = {Moczurad, W\l odzimierz},
     title = {Defect theorem in the plane},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {4},
     year = {2007},
     pages = {403-409},
     doi = {10.1051/ita:2007018},
     zbl = {pre05301988},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2007__41_4_403_0}
}
Moczurad, Włodzimierz. Defect theorem in the plane. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 41 (2007) no. 4, pp. 403-409. doi : 10.1051/ita:2007018. http://www.numdam.org/item/ITA_2007__41_4_403_0/

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