منابع مشابه
Perfect difference sets constructed from Sidon sets
A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...
متن کاملPerfect Skolem sets
A Skolem sequence is a sequence s1, s2, . . . , s2n (where si ∈ A = {1 . . . n}), each si occurs exactly twice in the sequence and the two occurrences are exactly si positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The problem of deciding which sets of the form A = {1 . . . n} are Skolem sets was solved by Thoralf Skolem in the late 1950’s. We stud...
متن کاملPerfect sets and collapsing continuum
Under Martin’s axiom, collapsing of the continuum by Sacks forcing S is characterized by the additivity of Marczewski’s ideal (see [4]). We show that the same characterization holds true if d = c proving that under this hypothesis there are no small uncountable maximal antichains in S. We also construct a partition of 2 into c perfect sets which is a maximal antichain in S and show that s-sets ...
متن کاملJulia Sets Are Uniformly Perfect
We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of loganthmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dinchlet. Using this we obtain a formula for the entropy of invanant harmonic measures on Julia sets. As a corollary we give a very short proof of ...
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 1987
ISSN: 0385-4035
DOI: 10.14492/hokmj/1381517829