Zero-sum Problems On The Sequence Index In Finite Cyclic Groups

Zero-sum problem is an important subfield of the combinatorial number theory,in which the combinatorial properties of the sequences in finite Abelian groups are the main object.The zero-sum problems on sequence index attract more attention in recent years.Zero-sum sequence is a sequence in Abelian group with sum zero.In direct zero-sum problems,we are to derive some combinatorial constants on zero-sum sequences,and on the contrary,we will consider the extremal sequences on the combinatorial constants,which belong to inverse zero-sum problems.In this thesis,we will consider some zero-sum problems on the sequence index in cyclic group Cn.In this thesis,there are four chapters:1.We introduce the background of zero-sum problem and the progress of zero-sum problems on the sequence index,describe the meaning of signs appearing in this paper,present basic concepts and theorems related to number theory and group theory,and give the structure arrangement of this paper.2.We summarize the development of the combinatorial constant l(Cn)and the structure of zero-sum sequences and zero-sum free sequences in finite cyclic groups Cn,and we consider the structure of zero-sum free sequences S of length |S|>(n+2)/3.3.We consentrate on the stucture of n-zero-sum free sequences.On the basis of the previous results,especially the proof on the structure of n-zero-sum free sequences with length bigger than (3n)/2-1,we partially give the description of the n-zero-sum free sequences S with |S|>(4n)/3-1.