A new extension of the Erdos-Heilbronn conjecture
Number Theory
2009-09-27 v3 Combinatorics
Abstract
Let A_1,...,A_n be finite subsets of a field F, and let f(x_1,...,x_n)=x_1^k+...+x_n^k+g(x_1,...,x_n)\in F[x_1,...,x_n] with deg g<k. We obtain a lower bound for the cardinality of {f(x_1,...,x_n): x_1\in A_1,...,x_n\in A_n, and x_i\not=x_j if i\not=j}. The result extends the Erdos-Heilbronn conjecture in a new way.
Keywords
Cite
@article{arxiv.0801.0080,
title = {A new extension of the Erdos-Heilbronn conjecture},
author = {Hao Pan and Zhi-Wei Sun},
journal= {arXiv preprint arXiv:0801.0080},
year = {2009}
}