k-Sums in abelian groups
Combinatorics
2012-06-27 v2 Group Theory
Number Theory
Abstract
Given a finite subset A of an abelian group G, we study the set k \wedge A of all sums of k distinct elements of A. In this paper, we prove that |k \wedge A| >= |A| for all k in {2,...,|A|-2}, unless k is in {2,|A|-2} and A is a coset of an elementary 2-subgroup of G. Furthermore, we characterize those finite subsets A of G for which |k \wedge A| = |A| for some k in {2,...,|A|-2}. This result answers a question of Diderrich. Our proof relies on an elementary property of proper edge-colourings of the complete graph.
Keywords
Cite
@article{arxiv.1110.1961,
title = {k-Sums in abelian groups},
author = {Benjamin Girard and Simon Griffiths and Yahya Ould Hamidoune},
journal= {arXiv preprint arXiv:1110.1961},
year = {2012}
}
Comments
15 pages