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  • Anton Cerný
  • 2002
The i-th symbol of the well-known infinite word of Thue on the alphabet {0, 1} can be characterized as the parity of the number of occurrences of the digit 1 in the binary representation of i. Generalized words of Thue are based on counting the parity of occurrences of an arbitrary word w ∈ {0, 1} * − 0 * in the binary representation of i. We provide here(More)
A word is called fair if it contains, for each pair of distinct symbols a, b, the same number of occurrences of the scattered subword ab as of ba. We prove that if the first k + 1 words in the sequence generated by a D0L system over a k-letter alphabet are fair then all words in the sequence are fair.