The structure of the spectra of Pisot numbers

For q (1,2), Erdös, Joó and Komornik studied the set: One item of interest that they examined is gap sizes of the form yk+1−yk. In particular, they were interested in lm(q) lim inf(yk+1−yk) and Lm(q) lim sup(yk+1−yk). This paper studies the distribution of the gap sizes yk+1−yk of sets Ym(q). The techniques of Feng and Wen are extended to study the frequency of various gap sizes. Some computations are made for various q. A precise description of the gap frequencies in Ym(q) is given when q is the golden ratio.