The arithmetic decomposition of central Cantor sets

Semi-fast convergent sequences and k-sums of central Cantor sets

“…where each x i repeats k times. The algebraic sums and differences of Cantor sets, in particular of sets of the form S k (C), were studied by many authors (see for example [1,7,9,12,[17][18][19]).…”

“…The central Cantor set C = E(2, 1; q) with q < 1 4 is the sum of three copies of E(1; q) = E(q n ). Despite the known fact that every central Cantor set is the algebraic sum of two central Cantor sets [18,Theorem 1], it is easy to observe that no central Cantor set is the sum of two copies of some central Cantor set.…”

When the algebraic difference of two central Cantor sets is an interval?

“…Algebraic differences and sums of Cantor sets were considered by many authors (e.g. [21], [10], [9], [15], [8], [1], [18], [14]). They appear for example in dynamical systems (see [16]), spectral theory (see [6], [20]) or number theory (see [8]).…”

Conditions for the difference set of a central Cantor set to be a Cantorval

“…We are interested in properties of the difference set C(λ)− C(λ). Several authors examined sums and differences of Cantor sets (see [2], [20] [21], [27], [29], [28]). Considerations about sums and differences of central Cantor sets were often based on the relationship between central Cantor sets and the achievement sets (i.e.…”

“…Recently, there have appeared a lot of interesting papers that explore properties of achievement sets, i.a. [5], [7], [27], [9], and [6].…”