Defect theorem in the plane
We consider the defect theorem in the context of labelled polyominoes, , 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).