On primitive words with non-primitive product

Author:

Echi OthmanORCID,Khalfallah AdelORCID,Kroumi DhakerORCID

Abstract

Let𝒜be an alphabet of sizen≥ 2. Our goal in this paper is to give a complete description of primitive wordspqover𝒜such thatpqis non-primitive. As an application, we will count the cardinality of the set(l,𝒜) of all couples (p,q) of distinct primitive words such that |p| = |q| =landpqis non-primitive, wherelis a positive integer. Then we give a combinatorial formula for the cardinalityε(n,l) of this set. The density in {(p,q) :p,qare distinct primitive words and |p| = |q| =l} of the set(l,𝒜) is also discussed.

Publisher

EDP Sciences

Subject

Computer Science Applications,General Mathematics,Software

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