The Olson constant represents the minimum positive integer with the property that every subset of cardinality contains a nonempty subset with vanishing sum. The problem of estimating is one of the oldest questions in additive combinatorics, with a long and interesting history even for the case .
We prove that for any fixed and , the Olson constant of satisfies the inequality
for all sufficiently large primes . This settles a conjecture of Hoi Nguyen and Van Vu.
"Zero-sum subsets in vector spaces over finite fields." Algebra Number Theory 16 (6) 1407 - 1421, 2022. https://doi.org/10.2140/ant.2022.16.1407