Note: Restricted set addition: The exceptional case of the Erdős--Heilbronn conjecture

Authors:
Gyula Károlyi
Affiliations:
Department of Algebra and Number Theory, Eötvös University, Pázmány P. sétány 1/C, Budapest H-1117, Hungary
Venue:
Journal of Combinatorial Theory Series A
Year:
2009

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Restricted sums of sets of cardinality 1 +p in a vector space over Fp

Discrete Mathematics
Combinatorial Nullstellensatz

Combinatorics, Probability and Computing

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Abstract

Let AB be nonempty subsets of the group of integers modulo a prime p. If p=|A|+|B|-2, then at least |A|+|B|-2 different residue classes can be represented as a+b, where a@?A, b@?B and ab. This result complements the solution of a problem of Erdos and Heilbronn obtained by Alon, Nathanson, and Ruzsa.