2022/02/18 by Othman Echi, Echi, Othman, Adel Khalfallah +3
Computer Science · #68Q45 #68R15 #Coding theory and cryptography #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2202.09091
openalex publication_date 2022/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be an alphabet of size n≥ 2. In this paper, we give a complete description of primitive words p≠ q over an alphabet A of size n≥2 such that pq is non-primitive and |p|=2|q|. In particular, if l is s a positive integer, we count the cardinality of the set E(l,A) of all couples (p,q) of primitive words such that |p|=2|q|=2l and pq is non-primitive. Then we give a combinatorial formula for this cardinality and its asymptotic behavior, as l or n goes to infinity.