Geodesic
Non-primitive words of the form 𝐩𝐪 𝐦
Echi, Othman1, 2 
1 King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics PO Box 5046, Dhahran 31261, Saudi Arabia.
2 University Tunis-El Manar. Faculty of Sciences of Tunis, Department of Mathematics, 2092 Tunis, Tunisia.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 3, pp. 141-166

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Let p,q be two distinct primitive words. According to Lentin−Schützenberger [9], the language p + q + contains at most one non-primitive word and if pq m is not primitive, then m≤2∣p∣ ∣q∣+3. In this paper we give a sharper upper bound, namely, m≤⌊∣p∣-2 ∣q∣+2⌋, where ⌊x⌋ stands for the floor of x.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2017012
Classification : 68R15
Keywords: Combinatorics on words, primitive word, primitive root

Echi, Othman 1, 2

1 King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics PO Box 5046, Dhahran 31261, Saudi Arabia.
2 University Tunis-El Manar. Faculty of Sciences of Tunis, Department of Mathematics, 2092 Tunis, Tunisia. 
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     title = {Non-primitive words of the form $\bold{p}\bold{q}^{\bold{m}}$},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {141--166},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {3},
     year = {2017},
     doi = {10.1051/ita/2017012},
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Echi, Othman. Non-primitive words of the form $\bold{p}\bold{q}^{\bold{m}}$. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 3, pp. 141-166. doi: 10.1051/ita/2017012

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