On subsequence sums of a zero-sum free sequence over finite abelian groups

Abstract

TextLet G be a finite abelian group and S be a sequence with elements of G. Let Σ(S)⊂G denote the set of group elements which can be expressed as a sum of a nonempty subsequence of S. We call S zero-sum free if 0∉Σ(S). In this paper, we study |Σ(S)| when S is a zero-sum free sequence of elements from G and 〈S〉 is not cyclic. We improve the results of A. Pixton and P. Yuan on this topic. In particular, we show that if S is a zero-sum free sequence with elements of G of length |S|=exp⁡(G)+3, then |Σ(S)|≥5exp⁡(G)−1, where exp⁡(G) denotes the exponent of G. This gives a positive answer to a case of a conjecture of B. Bollobás and I. Leader as well as to a case of a conjecture of W. Gao et al. VideoFor a video summary of this paper, please visit https://youtu.be/cvK4nZkY4lo.