A quadratic lower bound for subset sums

Let A be a finite nonempty subset of an additive abelian group G, and let \Sigma(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |\Sigma(A)| >= |H| + 1/64 |A H|^2 where H is the stabilizer of \Sigma(A). Our result implies that \Sigma(A) = Z/nZ for every set A of units of Z/nZ with |A| >= 8 \sqrt{n}. This consequence was first proved by Erd\H{o}s and Heilbronn for n prime, and by Vu (with a weaker constant) for general n.Comment: 12 page

Case Note: Slovenia

I Ips 7/2009,prepared by Kristina Brezjan (Student, Law Faculty of the University of Maribor) and reviewed by Dr. Liljana Selinšek. (Mobile telephone and SIM card; data of the incoming and outgoing calls of the appellants telephone number and of the base stations; whether illegally obtained evidence)

Case Note: Republic of Slovenia

I Up 505/2003. The Supreme Court of the Republic of Slovenia. Date: 18 June 2003