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 words is not a code then the words can be expressed as a product of at most 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 ( 1 or 1 rectangles).
Mots clés : 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}, pages = {403--409}, publisher = {EDP-Sciences}, volume = {41}, number = {4}, year = {2007}, doi = {10.1051/ita:2007018}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2007018/} }
TY - JOUR AU - Moczurad, Włodzimierz TI - Defect theorem in the plane JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2007 SP - 403 EP - 409 VL - 41 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2007018/ DO - 10.1051/ita:2007018 LA - en ID - ITA_2007__41_4_403_0 ER -
%0 Journal Article %A Moczurad, Włodzimierz %T Defect theorem in the plane %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2007 %P 403-409 %V 41 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2007018/ %R 10.1051/ita:2007018 %G en %F ITA_2007__41_4_403_0
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. http://www.numdam.org/articles/10.1051/ita:2007018/
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