Defect theorem in the plane

Moczurad, Włodzimierz

doi:10.1051/ita:2007018

Moczurad, Włodzimierz

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 4, pp. 403-409

Résumé

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 ( $n$ $\times$ 1 or 1 $\times$ $n$ rectangles).

DOI : 10.1051/ita:2007018

Classification : 68Q70, 68R15
Keywords: defect theorem, codes, polyominoes

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Moczurad, Włodzimierz. Defect theorem in the plane. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 4, pp. 403-409. doi: 10.1051/ita:2007018

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