论文标题
电路差异矩形
Circuit-Difference Matroids
论文作者
论文摘要
二进制矩阵的一种表征是，每对相交电路的对称差异是电路的不一致结合。本文认为电路差异矩形，即每对相交电路的对称差异是一个单一电路的矩形。我们的主要结果表明，当且仅当它包含一对偏斜电路时，连接的常规矩阵是电路差异。使用PFEIL的结果，这使我们能够明确确定所有常规电路差异矩形。在未成年人的情况下，电路差异的类别差异未关闭，但在串联未成年人中是关闭的。我们表征了该类无限的许多排除系列未成年人。
One characterization of binary matroids is that the symmetric difference of every pair of intersecting circuits is a disjoint union of circuits. This paper considers circuit-difference matroids, that is, those matroids in which the symmetric difference of every pair of intersecting circuits is a single circuit. Our main result shows that a connected regular matroid is circuit-difference if and only if it contains no pair of skew circuits. Using a result of Pfeil, this enables us to explicitly determine all regular circuit-difference matroids. The class of circuit-difference matroids is not closed under minors, but it is closed under series minors. We characterize the infinitely many excluded series minors for the class.
