tailieunhanh - Báo cáo toán hoc:" Subsequence Sums of Zero-sum-free Sequences Pingzhi Yuan "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Subsequence Sums of Zero-sum-free Sequences Pingzhi Yuan. | Subsequence Sums of Zero-sum-free Sequences Pingzhi Yuan School of Mathematics South China Normal University Guangzhou 510631 P. R. CHINA mcsypz@ Submitted Apr 25 2009 Accepted Jul 30 2009 Published Aug 7 2009 Mathematics Subject Classification 11B75 11B50 Abstract Let G be a finite abelian group and let S be a sequence of elements in G. Let f S denote the number of elements in G which can be expressed as the sum over a nonempty subsequence of S. In this paper we slightly improve some results of 10 on f S and we show that for every zero-sum-free sequences S over G of length S exp G 2 satisfying f S 4exp G 1. Key words Zero-sum problems Davenport s constant zero-sum-free sequence. 1 Introduction Let G be a finite abelian group written additively throughout the present paper. F G denotes the free abelian monoid with basis G the elements of which are called sequences in G . A sequence of not necessarily distinct elements from G will be written in the form S nn i 9i n eG gv S G F G where vg S 0 is called the multiplicity of g in S. Denote by S n the number of elements in S or the length of S and let supp S g G G vg S 0 be the support of S. We say that S contains some g G G if vg S 1 and a sequence T G F G is a subsequence of S if vg T vg S for every g G G denoted by T S. If T S then let ST-1 denote the sequence obtained by deleting the terms of T from S. Furthermore by ơ S we denote the sum of S . ơ S vi 1 9i YgeG vg S g G G . By S we denote the set consisting of all elements which can be expressed as a sum over a nonempty subsequence of S . ơ T T is a nonempty subsequence of S . Supported by the Guangdong Provincial Natural Science Foundation No. 8151027501000114 and NSF of China No. 10571180 . THE ELECTRONIC JOURNAL OF COMBINATORICS 16 2009 R97 1 We write f S I 52 S S for the subgroup of G generated by all the elements of S. Let S be a sequence in G. We call S a zero -sum sequence if ơ S 0 a zero sum-free sequence if ơ W 0 for any .