论文标题
$（{\ Mathbb z} _ {\ geq 0}）的补充对表征
Characterization of complementing pairs of $({\mathbb Z}_{\geq 0})^n$
论文作者
论文摘要
令$ a，b，c $为Abelian Group $ g $的子集。如果$ a，b \ subset c $和$ c $是$ a $ a $ a $ and $ b $的直接总和。 $（\ z _ {\ geq 0}）$ - 对以1950年的de bruijn为特征，$（\ z _ {\ geq 0}）^2 $ - niven在1971年的特征。我们表明，每一个$（\ z {\ geq 0}）^n $ - pair的特征在于加权树（如果是原始的），也就是说，它不是$（\ z {\ z {\ geq 0}）的笛卡尔产物，^p $ - p $ - p $ - （
Let $A, B, C$ be subsets of an abelian group $G$. A pair $(A, B)$ is called a $C$-pair if $A, B\subset C$ and $C$ is the direct sum of $A$ and $B$. The $(\Z_{\geq 0})$-pairs are characterized by de Bruijn in 1950 and the $(\Z_{\geq 0})^2$-pairs are characterized by Niven in 1971. In this paper, we characterize the $(\Z_{\geq 0})^n$-pairs for all $n\geq 1$. We show that every $(\Z_{\geq 0})^n$-pair is characterized by a weighted tree if it is primitive, that is, it is not a Cartesian product of a $(\Z_{\geq 0})^p$-pair and a $(\Z_{\geq 0})^q$-pair of lower dimensions.
