First distribution invariants and EKR theorems
Journal of Combinatorial Theory Series A
On a problem concerning the weight functions
European Journal of Combinatorics
A method to count the positive 3-subsets in a set of real numbers with non-negative sum
European Journal of Combinatorics
New results related to a conjecture of Manickam and Singhi
European Journal of Combinatorics
An improved bound for the Manickam-Miklós-Singhi conjecture
European Journal of Combinatorics
Nonnegative k-sums, fractional covers, and probability of small deviations
Journal of Combinatorial Theory Series B
Solution of a problem on non-negative subset sums
European Journal of Combinatorics
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The Manickam-Miklos-Singhi conjecture states that when n=4k, every multiset of n real numbers with nonnegative total sum has at least (n-1k-1)k-subsets with nonnegative sum. We develop a branching strategy using a linear programming formulation to show that verifying the conjecture for fixed values of k is a finite problem. To improve our search, we develop a zero-error randomized propagation algorithm. Using implementations of these algorithms, we verify a stronger form of the conjecture for all k@?7.