Erdős-Heilbronn conjecture

Let $A\subset{\mathbb{Z}}_{p}$ be a set of residues modulo $p$ , and let $h$ be a positive integer, then

h^{\wedge}\!A=\{\,a_{1}+a_{2}+\cdots+a_{h}\mid a_{1},a_{2},\ldots,a_{h}\text{ % are distinct elements of }A\,\}

has cardinality at least $\min(p,hk-h^{2}+1)$ . This was conjectured by Erdős and Heilbronn in 1964[1]. The first proof was given by Dias da Silva and Hamidoune in 1994.

References

1 Paul Erdős and Hans Heilbronn. On the addition of residue classes $\mod p$ . Acta Arith., 9:149–159, 1964. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0156.04801Zbl 0156.04801.
2 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry of Sumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.

Title	Erdős-Heilbronn conjecture
Canonical name	ErdHosHeilbronnConjecture
Date of creation	2013-03-22 13:38:15
Last modified on	2013-03-22 13:38:15
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	10
Author	bbukh (348)
Entry type	Theorem
Classification	msc 11B75
Related topic	CauchyDavenportTheorem