2018
DOI: 10.1016/j.jmaa.2018.05.065
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The arithmetic decomposition of central Cantor sets

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Cited by 13 publications
(12 citation statements)
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“…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]).…”
Section: Examplementioning
confidence: 99%
See 1 more Smart Citation
“…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]).…”
Section: Examplementioning
confidence: 99%
“…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.…”
Section: Examplementioning
confidence: 99%
“…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]).…”
Section: Introductionmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, there have appeared a lot of interesting papers that explore properties of achievement sets, i.a. [5], [7], [27], [9], and [6].…”
Section: Introductionmentioning
confidence: 99%