no. 3
Root clustering of words
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 267-280

Six kinds of both of primitivity and periodicity of words, introduced by Ito and Lischke [M. Ito and G. Lischke, Math. Log. Quart. 53 (2007) 91-106; Corrigendum in Math. Log. Quart. 53 (2007) 642-643], give rise to defining six kinds of roots of a nonempty word. For 1 ≤ k ≤ 6, a k-root word is a word which has exactly k different roots, and a k-cluster is a set of k-root words u where the roots of u fulfil a given prefix relationship. We show that out of the 89 different clusters that can be considered at all, in fact only 30 exist, and we give their quasi-lexicographically smallest elements. Also we give a sufficient condition for words to belong to the only existing 6-cluster. These words are also called Lohmann words. Further we show that, with the exception of a single cluster, each of the existing clusters contains either only periodic words, or only primitive words.

DOI : 10.1051/ita/2014009
Classification : 68Q45, 68R15
Keywords: periodicity of words, primitivity of words, roots of words, classification of words 
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     author = {Lischke, Gerhard},
     title = {Root clustering of words},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {267--280},
     year = {2014},
     publisher = {EDP Sciences},
     volume = {48},
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     doi = {10.1051/ita/2014009},
     mrnumber = {3302488},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita/2014009/}
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Lischke, Gerhard. Root clustering of words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 267-280. doi: 10.1051/ita/2014009

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