科研之友
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摘要
Let G be a finite abelian group of order n and let A subset of Z be non-empty. Generalizing a well-known constant, we define the Davenport constant of G with weight A, denoted by D-A(G), to be the least natural number k such that for any sequence (x(1), ..., x(k)) with x(i)is an element of G, there exists a non-empty subse quence (x(j1), ...., x(jl)) and a(1), ..., a(l) is an element of A such that Sigma(l)(i=1) a(i)x(ji)=0. Similarly, for any such A, E(A()G) is defined to be the least t is an element of N such that for all sequences (x(1), ..., x(t)) with x(i)is an element of G, there exist indices j(1), ..., j(n)is an element of N, 1 <= j(1)< ... < j(n)<= t, and v(1), ..., v(n)is an element of A with Sigma(n)(i=0) v(i)x(ji)=0. In the present paper, we establish a relation between the constants D-A(G) and E-A(G) under certain conditions. Our definitions are compatible with the previous generalizations for the particular group G=Z/nZ and the relation we establish had been conjectured in that particular case.
- 出版日期2008-1
- 单位南京师范大学
