|Publication ahead of print|
RAIRO-Theor. Inf. Appl.
|Published online||04 December 2017|
Non-primitive words of the form pqm
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.
Received: 8 November 2017
Accepted: 14 November 2017
Let p,q be two distinct primitive words. According to Lentin−Schützenberger , the language p+q+ contains at most one non-primitive word and if pqm is not primitive, then . In this paper we give a sharper upper bound, namely, where ⌊ x ⌋ stands for the floor of x.
Mathematics Subject Classification: 68R15
Key words: Combinatorics on words / primitive word / primitive root
© EDP Sciences 2017
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