Abstract:The Olson constant OL(F d p ) represents the minimum positive integer t with the property that every subset A ⊂ F d p of cardinality t contains a nonempty subset with vanishing sum. The problem of estimating OL(F d p ) is one of the oldest questions in additive combinatorics, with a long and interesting history even for the case d = 1.In this paper, we prove that for any fixed d ≥ 2 and ǫ > 0, the Olson constant of F d p satisfies the inequality OL(F d p ) ≤ (d − 1 + ǫ)p for all sufficiently large primes p. Th… Show more
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