Name
Abstract | ||
|---|---|---|
Let G be a finite abelian group of order n and let A⊆Z be non-empty. Generalizing a well-known constant, we define the Davenport constant of G with weight A, denoted by DA(G), to be the least natural number k such that for any sequence (x1,…,xk) with xi∈G, there exists a non-empty subsequence (xj1,…,xjl) and a1,…,al∈A such that ∑i=1laixji=0. Similarly, for any such set A, EA(G) is defined to be the least t∈N such that for all sequences (x1,…,xt) with xi∈G, there exist indices j1,…,jn∈N,1⩽j1<⋯<jn⩽t, and ϑ1,…,ϑn∈A with ∑i=1nϑixji=0. In the present paper, we establish a relation between the constants DA(G) and EA(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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.jcta.2007.03.004 | Journal of Combinatorial Theory, Series A |
Keywords | DocType | Volume |
Zero-sum problems,Davenport constant,The EGZ theorem | Journal | 115 |
Issue | ISSN | Citations |
1 | 0097-3165 | 4 |
PageRank | References | Authors |
0.55 | 3 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sukumar Das Adhikari | 1 | 23 | 6.47 |
| Yong-Gao Chen | 2 | 20 | 11.25 |