منابع مشابه
Supersequences, Rearrangements of Sequences, and the Spectrum of Bases in Additive Number Theory
The set A = {an}∞n=1 of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If an ∼ αn for some real number α > 0, then α is called an additive eigenvalue of order h. The additive spectrum of order h is the set N (h) consisting of all additive eigenvalues of order h. It is proved that there is a positive nu...
متن کاملSystems of Distinct Representatives and Minimal Bases in Additive Number Theory
The set A of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer is the sum of h elements of A . For example, the squares form an asymptotic basis of order 4 and the square-free numbers form an asymptotic basis of order 2 . If A is an asymptotic basis of order h, but no proper subset of A is an asymptotic basis of order h, then A is a minimal asymptotic ba...
متن کاملSome Problems in Additive Number Theory
(3) f(x) = (log x/log 2) + 0(1)? 1\Mloser and I asked : Is it true that f(2 11) >_ k+2 for sufficiently large k? Conway and Guy showed that the answer is affirmative (unpublished) . P. Erdös, Problems and results in additive number theory, Colloque, Théorie des Nombres, Bruxelles 1955, p . 137 . 2. Let 1 < a 1< . . . < ak <_ x be a sequence of integers so that all the sums ai,+ . . .+ais, i 1 <...
متن کاملFourier Analytic Methods in Additive Number Theory
In recent years, analytic methods have become prominent in additive number theory. In particular, finite Fourier analysis is well-suited to solve some problems that are too difficult for purely combinatorial techniques. Among these is Szemerédi’s Theorem, a statement regarding the density of integral sets and the existence of arithmetic progressions in those sets. In this thesis, we give a gene...
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1 . Introduction . In his paper [1], Erdös introduced the sequences of positive integers b 1 < b, < . . ., with (b ;, bj ) = 1, for i ~A j, and 'bi 1 < oo . With any such arbitrary sequence of integers, he associated the sequence {di} of all positive integers not divisible by any bj , and he showed that if b1 > 2, there exists a 0 < 1 (independent of the sequence {b i }) such that d i 1 di < d°...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.03.026