AbstractWe show that for n>k2(4elogk)k, every set {x1,⋯,xn} of n real numbers with ∑i=1nxi≥0 has at least (n−1k−1)k-element subsets of a non-negative sum. This is a substantial improvement on the best previously known bound of n>(k−1)(kk+k2)+k, proved by Manickam and Miklós [9] in 1987
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
AbstractFor a natural number k≥ 2 letρ=ρ(k) be the smallest natural number which does not dividek− 1...
Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of severa...
Suppose that we have a set of numbers x_1, ..., x_n which have nonnegative sum. How many subsets of ...
Suppose that we have a set of numbers x_1, ..., x_n which have nonnegative sum. How many subsets of ...
AbstractMore than twenty years ago, Manickam, Miklós, and Singhi conjectured that for any integers n...
AbstractWe show that for n>k2(4elogk)k, every set {x1,⋯,xn} of n real numbers with ∑i=1nxi≥0 has at ...
AbstractWe show that for everyk⩾3 the number of subsets of {1, 2, …, n} containing no solution tox1+...
AbstractLet {a1,a2,a3,…} be an unbounded sequence of positive integers with an+1/an approaching α as...
AbstractLet p be a prime and let L={l1,l2,…,ls} and K={k1,k2,…,kr} be two subsets of {0,1,2,…,p−1} s...
AbstractA 3-simplex is a collection of four sets A1,…,A4 with empty intersection such that any three...
AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not ...
AbstractIn this note we give a new upper bound for the largest size of subset of {1,2,…,n} not conta...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
Suppose that we have a set of numbers x1,..., xn which have nonnegative sum. How many subsets of k n...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
AbstractFor a natural number k≥ 2 letρ=ρ(k) be the smallest natural number which does not dividek− 1...
Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of severa...
Suppose that we have a set of numbers x_1, ..., x_n which have nonnegative sum. How many subsets of ...
Suppose that we have a set of numbers x_1, ..., x_n which have nonnegative sum. How many subsets of ...
AbstractMore than twenty years ago, Manickam, Miklós, and Singhi conjectured that for any integers n...
AbstractWe show that for n>k2(4elogk)k, every set {x1,⋯,xn} of n real numbers with ∑i=1nxi≥0 has at ...
AbstractWe show that for everyk⩾3 the number of subsets of {1, 2, …, n} containing no solution tox1+...
AbstractLet {a1,a2,a3,…} be an unbounded sequence of positive integers with an+1/an approaching α as...
AbstractLet p be a prime and let L={l1,l2,…,ls} and K={k1,k2,…,kr} be two subsets of {0,1,2,…,p−1} s...
AbstractA 3-simplex is a collection of four sets A1,…,A4 with empty intersection such that any three...
AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not ...
AbstractIn this note we give a new upper bound for the largest size of subset of {1,2,…,n} not conta...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
Suppose that we have a set of numbers x1,..., xn which have nonnegative sum. How many subsets of k n...
AbstractThe largest possible number of representations of an integer in thek-fold sumsetkA=A+…+Ais m...
AbstractFor a natural number k≥ 2 letρ=ρ(k) be the smallest natural number which does not dividek− 1...
Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of severa...
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