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A Polynomial Method Approach to Zero-Sum Subsets in F^2_p

Pohoata, Cosmin (2017) A Polynomial Method Approach to Zero-Sum Subsets in F^2_p. . (Unpublished)

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In this paper we prove that every subset of F^2_p 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(F^2_p) = p+OL(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.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:I would like to thank Fedor Petrov for helpful comments on a prior version of this preprint.
Record Number:CaltechAUTHORS:20200110-160359917
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100650
Deposited By: Tony Diaz
Deposited On:11 Jan 2020 00:32
Last Modified:11 Jan 2020 00:32

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