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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).
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