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- W4301372401 abstract "Let ||.|| be a norm in R^d whose unit ball is B. Assume that Vsubset B is a finite set of cardinality n, with sum_{v in V} v=0. We show that for every integer k with 0 le k le n, there exists a subset U of V consisting of k elements such that | sum_{v in U} v | le lceil d/2 rceil. We also prove that this bound is sharp in general. We improve the estimate to O(sqrt d) for the Euclidean and the max norms. An application on vector sums in the plane is also given." @default.
- W4301372401 created "2022-10-05" @default.
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- W4301372401 date "2015-02-13" @default.
- W4301372401 modified "2023-10-06" @default.
- W4301372401 title "Small subset sums" @default.
- W4301372401 doi "https://doi.org/10.48550/arxiv.1502.04027" @default.
- W4301372401 hasPublicationYear "2015" @default.
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