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

Text. Let G be a finite abelian group and S be a sequence with elements of G. Let Sigma(S) subset of 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 is not an element of Sigma(S). In this paper, we study vertical bar Sigma(S)vertical bar 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 vertical bar S vertical bar = exp (G) + 3, then vertical bar Sigma(S)vertical bar >= 5exp(G) - 1, where exp(G) denotes the exponent of G. This gives a positive answer to a case of a conjecture of B. Bollobas and I. Leader as well as to a case of a conjecture of W. Gao et al. Video. For a video summary of this paper, please visit hit https://youtu.be/cvK4nZkY4lo. (C) 2020 Elsevier Inc. All rights reserved.