LAUSR

Abstract Text Let 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 ) | ≥ 5 exp ⁡ ( 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 https://youtu.be/cvK4nZkY4lo .