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- W971691306 abstract "The course would not be complete without at least a very brief introduction to one of the most potent methods for solving additive questions—the polynomial method. There are numerous variations, but the core idea is to use polynomials, generally over a field, in order to solve, or help solve, a difficult additive problem. There are several results concerning polynomials that are often used in this regard. We present only the two most commonly used ones: The Combinatorial Nullstellensatz and the Chevalley-Warning Theorem. In its purest form, the method is unparalleled for tackling problems over a field that do not involve structural concerns, perhaps only asking for a lower bound of some sort. However, by augmenting the method with complicated combinatorial arguments, its power becomes greatly magnified to the point where these limitations can sometimes be overcome. We present the first major achievement of the method, which was a conjectured lower bound for the restricted sumset $$Ahat{+}B={a+b:; ain A,,bin B,,aneq b}, $$over a prime order group, originally proved by a more intricate argument involving exterior algebras. We will also give a recent punctured version of the Combinatorial Nullstellensatz due to Ball and Serra." @default.
- W971691306 created "2016-06-24" @default.
- W971691306 creator A5040241644 @default.
- W971691306 date "2013-01-01" @default.
- W971691306 modified "2023-09-26" @default.
- W971691306 title "The Polynomial Method: The Erdős-Heilbronn Conjecture" @default.
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- W971691306 doi "https://doi.org/10.1007/978-3-319-00416-7_22" @default.
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