Defect theorem in the plane
Institute of Computer Science, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland; email@example.com
Accepted: 7 December 2006
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).
Mathematics Subject Classification: 68Q70 / 68R15
Key words: Defect theorem / codes / polyominoes
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