2023/05/04 by Jeffrey Shallit · 1 citation
Computer Science · Mathematics · #math.NT #cs.DM #cs.FL
paper · pdf · doi:10.46298/cm.12627
We revisit a classic theorem of Frougny and Sakarovitch concerning automata for φ-representations, and show how to obtain it in a different and more computationally direct way. Using it, we can find simple, induction-free proofs of existing results in the literature about these representations, in a uniform and straightforward manner. In particular, we can easily and "automatically'' recover many of the results of recent papers of Dekking and Van Loon. We also obtain a number of new results on φ-representations.