Generating functionology
Fundamenta Informaticae - Special issue dedicated to A. Salomaa
Theoretical Computer Science
Multiple factorizations of words and defect effect
Theoretical Computer Science
Theory of Codes
A defect theorem for bi-infinite words
Theoretical Computer Science
A codicity undecidable problem in the plane
Theoretical Computer Science - Special issue: Tilings of the plane
Statistical properties of simple types
Mathematical Structures in Computer Science
Many aspects of defect theorems
Theoretical Computer Science - Words, languages and combinatorics
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Defect theorem, which provides a kind of dimension property for words, does not hold for two-dimensional figures (labelled polyominoes), except for some small sets. We thus turn to the analysis of asymptotic density of figure codes. Interestingly, it can often be proved to be 1, even in those cases where the defect theorem fails. Hence it reveals another weak dimension property which does hold for figures, i.e., non-codes are rare.We show that the asymptotic densities of codes among the following sets are all equal to 1: (ordinary) words, square figures and small sets of dominoes, where small refers to cardinality ≤ 3. The latter is a borderline case for the defect theorem and additionally exhibits interesting properties at different alphabet sizes.