Geodesic
Least periods of factors of infinite words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 165-178

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We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a sturmian word. In particular, the corresponding set for the Fibonacci word is the set of Fibonacci numbers. As a by-product of our results, we give several new proofs and tightenings of well-known properties of sturmian words.

DOI : 10.1051/ita:2008006
Classification : 68R15
Keywords: periodicity, Fibonacci word, Thue-Morse word, sturmian word 
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     title = {Least periods of factors of infinite words},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {165--178},
     publisher = {EDP-Sciences},
     volume = {43},
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     year = {2009},
     doi = {10.1051/ita:2008006},
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     zbl = {1162.68510},
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Currie, James D.; Saari, Kalle. Least periods of factors of infinite words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 165-178. doi: 10.1051/ita:2008006

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