Non-primitive words of the form $\bold{p}\bold{q}^{\bold{m}}$

Echi, Othman

doi:10.1051/ita/2017012

Non-primitive words of the form

𝐩 𝐪^{𝐦}

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.

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 3, pp. 141-166.

Résumé

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 $p q^{m}$ is not primitive, then $m \leq \frac{2 ∣ p ∣}{∣ q ∣} + 3$ . In this paper we give a sharper upper bound, namely, $m \leq ⌊ \frac{∣ p ∣ - 2}{∣ q ∣} + 2 ⌋,$ where $⌊ x ⌋$ stands for the floor of $x$ .

Reçu le : 2017-11-08
Accepté le : 2017-11-14

DOI : 10.1051/ita/2017012

Classification : 68R15
Mots clés : Combinatorics on words, primitive word, primitive root

Affiliations des auteurs :

Echi, Othman ^{1, 2}

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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. http://archive.numdam.org/articles/10.1051/ita/2017012/

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