Characterization of the algebraic difference of special affine Cantor sets

Abstract

We investigate some self-similar Cantor sets C(l, r, p), which we call S-Cantor sets, generated by numbers l, r, p ∈ N, l +r < p. We give a full characterization of the set C(l1, r1, p)−C(l2, r2, p) which can take one of the form: the interval [−1, 1], a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval. As corollaries we give examples of Cantor sets and Cantorvals, which can be easily described using some positional numeral systems.