2012/08/07 by Zuzana Masáková, Edita Pelantová, Masáková, Zuzana +1
Computer Science · Mathematics · #Algorithms and Data Compression #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1208.1413
9 pages
arxiv created 2012/08/07 · openalex publication_date 2012/08/07 · arxiv updated 2012/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given base γ and a digit set \mathcal B we consider optimal representations of a number x, as defined by Dajani at al. in 2012. For a non-integer negative base γ=-β<-1 and the digit set \mathcal Aβ:=0,1,...,\lceilβ\rceil-1 we derive the transformation which generates the optimal representation, if it exists. We show that -- unlike the case of negative integer base -- almost no x has an optimal representation. For a positive base γ=β>1 and the alphabet \mathcal Aβ we provide an alternative proof of statements obtained by Dajani et al.