论文标题
在$ \ mathbb z_n $的单位加权零和常数上
On unit-weighted zero-sum constants of $\mathbb Z_n$
论文作者
论文摘要
给定的$ a \ subseteq \ mathbb z_n $，常数$ c_a（n）$被定义为最小的自然数量$ k $，以使任何$ k $ ements in $ \ mathbb z_n $中的任何序列都具有连续项的$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a的元素。 $ c_ {u（n）}（n）$的值是奇数时知道的。我们给出不同的参数，以确定任何$ n $的$ c_ {u（n）}（n）$的值。 A $C$-extremal sequence for $U(n)$ is a sequence in $\mathbb Z_n$ whose length is $C_{U(n)}(n)-1$ and which does not have any $U(n)$-weighted zero-sum subsequence having consecutive terms.当$ n $的功率为2时，我们表征了$ u（n）$的$ c $ -Extremal序列。对于任何$ n $，我们确定$ c_a（n）$的值，其中$ a $是$ \ mathbb z_n $的所有奇数（甚至所有）元素的集合，当$ a = a = \ a = \ a = \ where {1,2 $ rdots $ rdots $ rdots，rd。
Given $A\subseteq\mathbb Z_n$, the 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 having consecutive terms. The value of $C_{U(n)}(n)$ is known when $n$ is odd. We give a different argument to determine the value of $C_{U(n)}(n)$ for any $n$. A $C$-extremal sequence for $U(n)$ is a sequence in $\mathbb Z_n$ whose length is $C_{U(n)}(n)-1$ and which does not have any $U(n)$-weighted zero-sum subsequence having consecutive terms. We characterize the $C$-extremal sequences for $U(n)$ when $n$ is a power of 2. For any $n$, we determine the value of $C_A(n)$ where $A$ is the set of all odd (or all even) elements of $\mathbb Z_n$ and also when $A=\{1,2,\ldots,r\}$ where $r<n$.
