2017/01/17 by Zuzana Krčmáriková, Krčmáriková, Zuzana, Wolfgang Steiner +3
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory
paper · doi:10.48550/arxiv.1701.04609
openalex publication_date 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers β having the negative finiteness property, that is the set of finite (-β)-expansions is equal to ℤ[β-1]. For a class of numbers including the Tribonacci number, we compute the maximal length of the fractional parts arising in the addition and subtraction of (-β)-integers. We also give conditions excluding the negative finiteness property.