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A Cauchy-Davenport theorem for linear maps
We prove a version of the Cauchy-Davenport theorem for general linear maps.
For subsets of the finite field , the classical
Cauchy-Davenport theorem gives a lower bound for the size of the sumset
in terms of the sizes of the sets and . Our theorem considers a general
linear map , and subsets , and gives a lower bound on the size of in terms of the sizes of the sets .
Our proof uses Alon's Combinatorial Nullstellensatz and a variation of the
polynomial method.Comment: 16 pages, 0 figure