On sums of a Sidon-sequence
نویسندگان
چکیده
منابع مشابه
On Uniformly Approximable Sidon Sets
Let G be a compact abelian group and let T be the character group of G. Suppose £ is a subset of T. A trigonometric polynomial f on G is said to be an ^-polynomial if its Fourier transform / vanishes off E. The set E is said to be a Sidon set if there is a positive number B such that 2^xeb |/(X)| á-B||/||u for all E-polynomials /; here, ||/||„ = sup{ |/(x)| : xEG}. In this note we shall discuss...
متن کاملOn Subsequence Sums of a Zero-sum Free Sequence II
Let G be an additive finite abelian group with exponent exp(G) = n. For a sequence S over G, let f(S) denote the number of non-zero group elements which can be expressed as a sum of a nontrivial subsequence of S. We show that for every zero-sum free sequence S over G of length |S| = n + 1 we have f(S) ≥ 3n − 1.
متن کاملOn Subsequence Sums of a Zero-sum Free Sequence
Let G be a finite abelian group with exponent m, and let S be a sequence of elements in G. Let f(S) denote the number of elements in G which can be expressed as the sum over a nonempty subsequence of S. In this paper, we show that, if |S| = m and S contains no nonempty subsequence with zero sum, then f(S) ≥ 2m − 1. This answers an open question formulated by Gao and Leader. They proved the same...
متن کاملOn Multiplicative Sidon Sets
Fix integers b > a ≥ 1 with g := gcd(a, b). A set S ⊆ N is {a, b}-multiplicative if ax 6= by for all x, y ∈ S. For all n, we determine an {a, b}-multiplicative set with maximum cardinality in [n], and conclude that the maximum density of an {a, b}-multiplicative set is b b+g . Erdős [2, 3, 4] defined a set S ⊆ N to be multiplicative Sidon1 if ab = cd implies {a, b} = {c, d} for all a, b, c, d ∈...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1991
ISSN: 0022-314X
DOI: 10.1016/0022-314x(91)90083-n