Pohoata, Cosmin (2017) A Polynomial Method Approach to Zero-Sum Subsets in F^2_p. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200110-160359917
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Abstract
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 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200110-160359917 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 100650 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 11 Jan 2020 00:32 | ||||||
| Last Modified: | 11 Jan 2020 00:32 |
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