Published online by Cambridge University Press: 17 August 2007
We consider the defect theorem in the context of labelledpolyominoes, i.e., two-dimensional figures. The classical version ofthis property states that if a set of n words is not a code thenthe words can be expressed as a product of at most n - 1 words, thesmaller set being a code. We survey several two-dimensionalextensions exhibiting the boundaries where the theorem fails. Inparticular, we establish the defect property in the case of threedominoes (n × 1 or 1 × n rectangles).