2023/09/06 by Jakub Konieczny, Konieczny, Jakub, Clemens Müllner +1 · 1 citation
Computer Science · #Advanced Algebra and Logic #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2309.03180
openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We fully classify automatic sequences a over a finite alphabet Ω with the property that each word over Ω appears is a along an arithmetic progression. Using the terminology introduced by Avgustinovich, Fon-Der-Flaass and Frid, these are the automatic sequences with the maximal possible arithmetical subword complexity. More generally, we obtain an asymptotic formula for arithmetical (and even polynomial) subword complexity of a given automatic sequence a.