منابع مشابه
Perfect 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 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 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 ...
متن کاملNearly perfect sets in graphs
In a graph G = (V; E), a set of vertices S is nearly perfect if every vertex in V ? S is adjacent to at most one vertex in S. Nearly perfect sets are closely related to 2-packings of graphs, strongly stable sets, dominating sets and eecient dominating sets. We say a nearly perfect set S is 1-minimal if for every vertex u in S, the set S ? fug is not nearly perfect. Similarly, a nearly perfect s...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1978
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90169-3