论文标题
与雅各比符号有关的极端序列
Extremal sequences related to the Jacobi symbol
论文作者
论文摘要
For a weight-set $A\subseteq \mathbb Z_n$, the $A$-weighted zero-sum constant $C_A(n)$ is defined to be the smallest natural number $k$, such that any sequence of $k$ elements in $\mathbb Z_n$ has an $A$-weighted zero-sum subsequence of consecutive terms.一系列长度$ c_a（n）-1 $ in $ \ mathbb z_n $，该$没有任何$ a $ a $ wate的零和连续项的零子序列将称为$ a $ a $ a $的$ c $ - 超级序列。 令$ \ big（\ frac {x} {n} \ big）$表示$ x \ in \ mathbb z_n $的jacobi符号。我们表征了重量集$ s（n）= \ big \ {\ {\，x \ in U（n）中的$ c $ -Extremal序列： u（n）：\ big（\ frac {x} {n} \ big）= \ big（\ frac {x} {p} {p} {p} \ big）\，\ big \} $，其中$ p $是$ n $的主要除法。我们可以以类似于$ c $ -ESTREMAL序列的定义来定义这些权重集的$ d $ - 超级序列。我们还表征了这些序列。
For a weight-set $A\subseteq \mathbb Z_n$, the $A$-weighted zero-sum constant $C_A(n)$ is defined to be the smallest natural number $k$, such that any sequence of $k$ elements in $\mathbb Z_n$ has an $A$-weighted zero-sum subsequence of consecutive terms. A sequence of length $C_A(n)-1$ in $\mathbb Z_n$ which does not have any $A$-weighted zero-sum subsequence of consecutive terms will be called a $C$-extremal sequence for $A$. Let $\big(\frac{x}{n}\big)$ denote the Jacobi symbol of $x\in\mathbb Z_n$. We characterize the $C$-extremal sequences for the weight-set $S(n)=\big\{\,x\in U(n):\big(\frac{x}{n}\big)=1\,\big\}$ and for the weight-set $L(n;p)=\big\{\,x\in U(n):\big(\frac{x}{n}\big)=\big(\frac{x}{p}\big)\,\big\}$ where $p$ is a prime divisor of $n$. We can define $D$-extremal sequences for these weight-sets in a way analogous to the definition of $C$-extremal sequences. We also characterize these sequences.
