2025/11/25 by K. Ernest Bognini, Bognini, K. Ernest, Hamdi Ammar +1
Computer Science · #11B85 #37B10 #68Q45 #68R15 #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2511.20881
openalex publication_date 2025/11/25 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28
In this paper, we study some new factorizations of period-doubling sequences over a k-letter alphabet, where k≥ 2. First, we define the combinatorial and arithmetic properties of these sequences. Then, we define the kernel words of period-doubling sequences and demonstrate how to factorize a binary sequence using its kernel words. Next, we define gap sequences for period-doubling sequences and explore their relationship with kernel words. Lastly, we present a factorization of period-doubling sequences for k≥ 3 based on kernel words and gap sequences.