论文标题
关于加权零和子序列的数量
On the Number of Weighted Zero-sum Subsequences
论文作者
论文摘要
让$ g $为有限的添加剂ABELIAN集团，带有指数$ d^kn，d，n> 1，$ $ k $ a正整数。对于$ s $ a $ g $和$ a = \ {1,2，\ ldots，d^kn-1 \} \ setMinus \ {d^kn/d^i：i \ in [1，k] \}，$，我们调查了数量$ n_ {a，0} $的$ n数字$，$ n数字$，特别是，我们证明$ n_ {a，0}（s）\ ge 2^{| s | -d_a（g）+1}，其中$ d_a（g）$是$ a $ a $ a watered davenport常数。我们还表征了某些群体相等性的极端序列的结构。
Let $G$ be a finite additive abelian group with exponent $d^kn, d,n>1,$ and $k$ a positive integer. For $S$ a sequence over $G$ and $A=\{1,2,\ldots,d^kn-1\}\setminus\{d^kn/d^i:i\in[1,k]\}, $ we investigate the lower bound of the number $N_{A,0}(S)$, which denotes the number of $A$-weighted zero-sum subsequences of $S.$ In particular, we prove that $N_{A,0}(S)\ge 2^{|S|-D_A(G)+1},$ where $D_A(G)$ is the $A$-weighted Davenport Constant. We also characterize the structures of the extremal sequences for which equality holds for some groups.
