AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not divisible by q for each q⩾2. Let f(n,r) denote the maximum cardinality of an r-set A ⊂ {1,2,…,n} having no subset sum Σεiai(εi=0 or 1, aiϵA) equal to a power of two. In this paper estimates for f(n,r) are obtained. We prove that limr→∞αr=0, where αr=limn→∞f(n,r)n. This result verifies a conjecture of Erdős and Freiman (1990)
Moulton and Develin have investigated the notion of representing various sets S of positive integers...
AbstractWe show that for everyk⩾3 the number of subsets of {1, 2, …, n} containing no solution tox1+...
A set S of positive integers has distinct subset sums if there are 2 jSj distinct elements of the ...
AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not ...
Given a set of n real numbers, if the sum of the elements of every subset of size larger than k is n...
AbstractWe show that for n>k2(4elogk)k, every set {x1,⋯,xn} of n real numbers with ∑i=1nxi≥0 has at ...
Alon N, Aydinian H, Huang H. Maximizing the Number of Nonnegative Subsets. SIAM Journal on Discrete ...
AbstractLet A be a set of nonnegative integers. For h≥2, denote by hA the set of all the integers re...
We give tight lower bounds on the cardinality of the sumset of two finite, nonempty subsets A, B ⊆ R...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
AbstractWe give tight lower bounds on the cardinality of the sumset of two finite, nonempty subsets ...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
AbstractLet F be an arbitrary field. Letpbe the characteristic of F in case of finite characteristic...
AbstractSuppose that A is a finite set-system on N points, and for everytwo different A, A′ϵ A we ha...
Moulton and Develin have investigated the notion of representing various sets S of positive integers...
AbstractWe show that for everyk⩾3 the number of subsets of {1, 2, …, n} containing no solution tox1+...
A set S of positive integers has distinct subset sums if there are 2 jSj distinct elements of the ...
AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not ...
Given a set of n real numbers, if the sum of the elements of every subset of size larger than k is n...
AbstractWe show that for n>k2(4elogk)k, every set {x1,⋯,xn} of n real numbers with ∑i=1nxi≥0 has at ...
Alon N, Aydinian H, Huang H. Maximizing the Number of Nonnegative Subsets. SIAM Journal on Discrete ...
AbstractLet A be a set of nonnegative integers. For h≥2, denote by hA the set of all the integers re...
We give tight lower bounds on the cardinality of the sumset of two finite, nonempty subsets A, B ⊆ R...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
AbstractWe give tight lower bounds on the cardinality of the sumset of two finite, nonempty subsets ...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
summary:Let $n > m \geq 2$ be positive integers and $n=(m+1) \ell +r$, where $0 \leq r \leq m.$ Let ...
AbstractLet F be an arbitrary field. Letpbe the characteristic of F in case of finite characteristic...
AbstractSuppose that A is a finite set-system on N points, and for everytwo different A, A′ϵ A we ha...
Moulton and Develin have investigated the notion of representing various sets S of positive integers...
AbstractWe show that for everyk⩾3 the number of subsets of {1, 2, …, n} containing no solution tox1+...
A set S of positive integers has distinct subset sums if there are 2 jSj distinct elements of the ...
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