Weighted Davenport’s constant and the weighted EGZ Theorem

Publication year: 2011
Source: Discrete Mathematics, Volume 311, Issue 17, 6 September 2011, Pages 1940-1947

Xiangneng, Zeng , Pingzhi, Yuan

Let G∗,G be finite abelian groups with nontrivial homomorphism group . Let Ψ be a non-empty subset of . Let DΨ(G) denote the minimal integer, such that any sequence over G∗ of length DΨ(G) must contain a nontrivial subsequence s1,…,sr, such that for some ψi∈Ψ. Let EΨ(G) denote the minimal integer such that any sequence over G∗ of length EΨ(G) must contain a nontrivial subsequence of length G,s1,…,sG, such that for some ψi∈Ψ. In this paper, we show that EΨ(G)=G+DΨ(G)−1.