Dense infinite $B_h$ sequences
نویسندگان
چکیده
منابع مشابه
DENSE INFINITE Bh SEQUENCES
For h = 3 and h = 4 we prove the existence of infinite Bh sequences B with counting function B(x) = x √ (h−1)2+1−(h−1)+o(1). This result extends a construction of I. Ruzsa for B2 sequences.
متن کاملDense admissible sequences
A sequence of integers in an interval of length x is called admissible if for each prime there is a residue class modulo the prime which contains no elements of the sequence. The maximum number of elements in an admissible sequence in an interval of length x is denoted by %∗(x). Hensley and Richards showed that %∗(x) > π(x) for large enough x. We increase the known bounds on the set of x satisf...
متن کاملSophisticated Infinite Sequences
In this paper we revisit the notion of sophistication for infinite sequences. Koppel defined sophistication of an object as the length of the shortest (finite) total program (p) that with some (finite or infinite) data (d) produce it and |p|+ |d| is smaller than the shortest description of the object plus a constant. However the notion of “description of infinite sequences” is not appropriately...
متن کاملInfinite Sidon sequences
We give the first explicit construction of an infinite Sidon sequence A with A(x) x for some c > 1/3. Our method allows to take c = √ 2− 1. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to Bh sequences when h ≥ 3. In these case our constructions are not explicit but they give the first improvements on the...
متن کاملLimits of dense graph sequences
We show that if a sequence of dense graphs Gn has the property that for every fixed graph F , the density of copies of F in Gn tends to a limit, then there is a natural “limit object”, namely a symmetric measurable function W : [0, 1] → [0, 1]. This limit object determines all the limits of subgraph densities. Conversely, every such function arises as a limit object. We also characterize graph ...
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: Publicacions Matemàtiques
سال: 2015
ISSN: 0214-1493
DOI: 10.5565/publmat_59115_04