Erdős and Heilbronn (Erdős and Graham 1980) posed the problem of estimating from below the number of sums 
where 
and 
range over given sets 
of residues modulo a prime 
, so that 
. Dias da Silva and Hamidoune (1994) gave a solution, and
Alon et al. (1995) developed a polynomial method that allows one to handle
restrictions of the type 
, where 
is a polynomial in two variables over 
.
Erdős-Heilbronn Conjecture
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References
Alon, N.; Nathanson, M. B.; and Ruzsa, I. Z. "Adding Distinct Congruence Classes Modulo a Prime." Amer. Math. Monthly 102, 250-255, 1995.Dias da Silva, J. A. and Hamidoune, Y. O. "Cyclic Spaces for Grassmann Derivatives and Additive Theory." Bull. London Math. Soc. 26, 140-146, 1994.Erdős, P. and Graham, R. L. Old and New Problems and Results in Combinatorial Number Theory. Geneva, Switzerland: L'Enseignement Mathématique Université de Genève, Vol. 28, 1980.Lev, V. F. "Restricted Set Addition in Groups, II. A Generalization of the Erdős-Heilbronn Conjecture." Electronic J. Combinatorics 7, No. 1, R4, 1-10, 2000. http://www.combinatorics.org/Volume_7/Abstracts/v7i1r4.html.Referenced on Wolfram|Alpha
Erdős-Heilbronn ConjectureCite this as:
Weisstein, Eric W. "Erdős-Heilbronn Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Erdos-HeilbronnConjecture.html