Non-primitive words of the form p q m

Othman Echi

doi:10.1051/ita/2017012

Non-primitive words of the form p q ^m

Othman Echi^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 \hbox{$m\leq \dfrac{2\mid p\mid}{\mid q\mid}+3$}. In this paper we give a sharper upper bound, namely, \hbox{$m\leq \lfloor\dfrac{\mid p\mid-2}{\mid q\mid}+2\rfloor,$} where âŒŠ x âŒ stands for the floor of x.

Original language	English
Pages (from-to)	141-166
Number of pages	26
Journal	RAIRO - Theoretical Informatics and Applications
Volume	51
Issue number	3
DOIs	https://doi.org/10.1051/ita/2017012
State	Published - 1 Jul 2017

Bibliographical note

Publisher Copyright:
© EDP Sciences 2017.

Keywords

Combinatorics on words
Primitive root
Primitive word

ASJC Scopus subject areas

Software
General Mathematics
Computer Science Applications

Access to Document

10.1051/ita/2017012

Cite this

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title = "Non-primitive words of the form p q m",

abstract = "Let p,q be two distinct primitive words. According to Lentin-Sch{\"u}tzenberger [9], the language p+q+ contains at most one non-primitive word and if pqm is not primitive, then \textbackslash{}hbox\{\$m\textbackslash{}leq \textbackslash{}dfrac\{2\textbackslash{}mid p\textbackslash{}mid\}\{\textbackslash{}mid q\textbackslash{}mid\}+3\$\}. In this paper we give a sharper upper bound, namely, \textbackslash{}hbox\{\$m\textbackslash{}leq \textbackslash{}lfloor\textbackslash{}dfrac\{\textbackslash{}mid p\textbackslash{}mid-2\}\{\textbackslash{}mid q\textbackslash{}mid\}+2\textbackslash{}rfloor,\$\} where {\^a}{\OE}{\v S} x {\^a}{\OE} stands for the floor of x.",

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note = "Publisher Copyright: {\textcopyright} EDP Sciences 2017.",

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doi = "10.1051/ita/2017012",

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N1 - Publisher Copyright: © EDP Sciences 2017.

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N2 - 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 pqm is not primitive, then \hbox{$m\leq \dfrac{2\mid p\mid}{\mid q\mid}+3$}. In this paper we give a sharper upper bound, namely, \hbox{$m\leq \lfloor\dfrac{\mid p\mid-2}{\mid q\mid}+2\rfloor,$} where âŒŠ x âŒ stands for the floor of x.

AB - 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 pqm is not primitive, then \hbox{$m\leq \dfrac{2\mid p\mid}{\mid q\mid}+3$}. In this paper we give a sharper upper bound, namely, \hbox{$m\leq \lfloor\dfrac{\mid p\mid-2}{\mid q\mid}+2\rfloor,$} where âŒŠ x âŒ stands for the floor of x.

KW - Combinatorics on words

KW - Primitive root

KW - Primitive word

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