论文标题
组合衍生的曲霉
Combinatorial Derived Matroids
论文作者
论文摘要
令$ m $为带电路$ \ MATHCAL {C}（M）$的任意矩阵。我们提出了一个定义的定义，该定义是其地面设置$ \ MATHCAL {C}（M）$的定义。与这种定义的先前尝试不同，我们的定义适用于任意的矩阵，并且完全是组合。我们证明，$δm$的排名在上面的$ | m | -r（m）$中，当时仅在连接$ m $时才连接。我们计算示例，包括均匀基质的衍生曲霉，VámosMatroid和图形矩阵$ M（K_4）$。我们制定了将我们的构造与先前的衍生成曲霉定义有关的猜想。
Let $M$ be an arbitrary matroid with circuits $\mathcal{C}(M)$. We propose a definition of a derived matroid $δM$ that has as its ground set $\mathcal{C}(M)$. Unlike previous attempts of such a definition, our definition applies to arbitrary matroids, and is completely combinatorial. We prove that the rank of $δM$ is bounded from above by $|M|-r(M)$, that it is connected if and only if $M$ is connected. We compute examples including the derived matroids of uniform matroids, the Vámos matroid and the graphical matroid $M(K_4)$. We formulate conjectures relating our construction to previous definitions of derived matroids.
