论文标题
在亚伯群体上的成绩单中的匹配
Matchings in matroids over abelian groups
论文作者
论文摘要
我们制定并证明了有关组中匹配的结果的矩形类似物。 Abelian Group $（g，+）$的匹配是两个有限的子集$ a，b $ a，b $ g $满足$ a+a+a+f（a）\ notin a $ a $ a $ a \ in a $中的$ a \。组$ g $具有匹配属性，如果每两个有限的子集$ a，b \ subset g $与$ 0 \ notin b $相同，则存在从$ a $ a $到$ b $的匹配。在[19]中，当且仅当它不含扭转或循环时，Abelian群体具有匹配属性。在这里，我们考虑了在Matroid设置中的类似问题。我们引入了与Abelian $ g $的子集之间的Matroids之间的匹配概念，我们获得了存在此类匹配的标准。我们的工具是矩阵理论，群体理论和添加数理论的经典定理。
We formulate and prove matroid analogues of results concerning matchings in groups. A matching in an abelian group $(G,+)$ is a bijection $f:A\to B$ between two finite subsets $A,B$ of $G$ satisfying $a+f(a)\notin A$ for all $a\in A$. A group $G$ has the matching property if for every two finite subsets $A,B \subset G$ of the same size with $0 \notin B$, there exists a matching from $A$ to $B$. In [19] it was proved that an abelian group has the matching property if and only if it is torsion-free or cyclic of prime order. Here we consider a similar question in a matroid setting. We introduce an analogous notion of matching between matroids whose ground sets are subsets of an abelian group $G$, and we obtain criteria for the existence of such matchings. Our tools are classical theorems in matroid theory, group theory and additive number theory.
