| Issue |
RAIRO-Theor. Inf. Appl.
Volume 56, 2022
|
|
|---|---|---|
| Article Number | 4 | |
| Number of page(s) | 11 | |
| DOI | https://doi.org/10.1051/ita/2022004 | |
| Published online | 21 February 2022 | |
On primitive words with non-primitive product
Department of Mathematics, King Fahd University of Petroleum and Minerals,
Dhahran
31261, Saudi Arabia.
* Corresponding author: othechi@yahoo.com
Received:
16
August
2021
Accepted:
1
February
2022
Let 𝒜 be an alphabet of size n ≥ 2. Our goal in this paper is to give a complete description of primitive words p≠q over 𝒜 such that pq is non-primitive. As an application, we will count the cardinality of the set ℰ(l,𝒜) of all couples (p, q) of distinct primitive words such that |p| = |q| = l and pq is non-primitive, where l is a positive integer. Then we give a combinatorial formula for the cardinality ε(n, l) of this set. The density in {(p, q) : p, q are distinct primitive words and |p| = |q| = l} of the set ℰ(l,𝒜) is also discussed.
Mathematics Subject Classification: 68R15 / 68Q45
Key words: Combinatorics on words / Primitive words / primitive root / Möbius inversion formula
© The authors. Published by EDP Sciences, 2022
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