Let A,B be different nonempty subsets of the group of integers modulo a prime p. If p is not smaller than |A|+|B|-2, then at least this many residue classes can be represented as a+b, where a and b are different elements of A and B, respectively. This result complements the solution of a problem of Erdos and Heilbronn obtained by Alon, Nathanson, and Ruzsa.
Additional Metadata
Keywords Erdos-Heilbronn conjecture, Structural theory of set addition, Combinatorial Nullstellensatz, restricted set addition
MSC ) (msc 11B50), Other combinatorial number theory (msc 11B75)
Publisher Academic Press
Journal Journal of Combinatorial Theory - Series A
Project Spinoza prijs Lex Schrijver
Citation
Karolyi, G. (2009). Restricted set addition: The exceptional case of the Erdos-Heilbronn conjecture. Journal of Combinatorial Theory - Series A, 116(3), 741–746.