A new extension of the Erdos-Heilbronn conjecture

作者：Pan Hao^*; Sun Zhi Wei

来源：Journal of Combinatorial Theory - Series A, 2009, 116(8): 1374-1381.

DOI：10.1016/j.jcta.2009.04.001

• Erdos-Heilbronn conjecture
• Combinatorial Nullstellensatz
• Value sets of polynomials

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)) is an element of F[x(1), ... x(n)] with deg g < k. We obtain a lower bound for the cardinality of {f(x1,...,x(n)): x(1) is an element of A(1),..., x(n) is an element of A(n), and x(i) not equal x(j) if i not equal j}. The result extends the Erdos-Heilbronn conjecture in a new way.

• 出版日期2009-11
• 单位南京大学