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On subwords of infinite words

✍ Scribed by Lucian Ilie

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
175 KB
Volume
63
Category
Article
ISSN
0166-218X

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πŸ“œ SIMILAR VOLUMES

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Lutz Priese raised the following conjecture: Almost all words of length n over a finite alphabet A with m letters contain as subwords all words of length [log log n] over A as n -+ co. In this note we prove that this property holds for subwords of length k(n) over A provided lim,, m k(n)/logn = 0.

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We show that an infinite word s satisfies s = uoutu2 . . . with all ui being different nonempty words and their set being a biprefix code if and only if s is not ultimately periodic. We give also related results, considering in particular arbitrary codes, infix codes and the case of two-sided infini