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- W4297836006 abstract "In this paper we prove that every subset of $mathbb{F}_p^2$ meeting all $p+1$ lines passing through the origin has a zero-sum subset. This is motivated by a result of Gao, Ruzsa and Thangadurai which states that $OL(mathbb{F}_{p}^{2})=p+OL(mathbb{F}_{p})-1$, for sufficiently large primes $p$. Here $OL(G)$ denotes the so-called Olson constant of the additive group $G$ and represents the smallest integer such that no subset of cardinality $OL(G)$ is zero-sum-free. Our proof is in the spirit of the Combinatorial Nullstellensatz." @default.
- W4297836006 created "2022-10-01" @default.
- W4297836006 creator A5042386416 @default.
- W4297836006 date "2017-03-01" @default.
- W4297836006 modified "2023-09-30" @default.
- W4297836006 title "A Polynomial Method Approach to Zero-Sum Subsets in $mathbb{F}_{p}^{2}$" @default.
- W4297836006 doi "https://doi.org/10.48550/arxiv.1703.00414" @default.
- W4297836006 hasPublicationYear "2017" @default.
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