Subset sums in abelian groups
Combinatorics
2014-07-01 v1 Group Theory
Number Theory
Abstract
Denoting by Sigma(S) the set of subset sums of a subset S of a finite abelian group G, we prove that |Sigma(S)| >= |S|(|S|+2)/4-1 whenever S is symmetric, |G| is odd and Sigma(S) is aperiodic. Up to an additive constant of 2 this result is best possible, and we obtain the stronger (exact best possible) bound in almost all cases. We prove similar results in the case |G| is even. Our proof requires us to extend a theorem of Olson on the number of subset sums of anti-symmetric subsets S from the case of Z_p to the case of a general finite abelian group. To do so, we adapt Olson's method using a generalisation of Vosper's Theorem proved by Hamidoune and Plagne.
Cite
@article{arxiv.1112.1929,
title = {Subset sums in abelian groups},
author = {Eric Balandraud and Benjamin Girard and Simon Griffiths and Yahya Ould Hamidoune},
journal= {arXiv preprint arXiv:1112.1929},
year = {2014}
}
Comments
22 pages, submitted