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Erdős-Heilbronn Conjecture


Erdős and Heilbronn (Erdős and Graham 1980) posed the problem of estimating from below the number of sums a+b where a in A and b in B range over given sets A,B subset= Z/pZ of residues modulo a prime p, so that a!=b. 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 f(a,b)!=0, where f is a polynomial in two variables over Z/pZ.


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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.

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Erdős-Heilbronn Conjecture

Cite this as:

Weisstein, Eric W. "Erdős-Heilbronn Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Erdos-HeilbronnConjecture.html

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