自由积、极值拟阵以及完美拟阵设计的推广
Free products, extremal matroids, and a generalization of perfect matroid designs
浏览论文内容
中文总结 AI 辅助
研究如何从拟阵\(M\)和\(M'\)在其多面体中的点得到自由积\(M\square M'\)在相应多面体中的点，证明若\(M\square M'\)极值则\(M\)和\(M'\)极值，反之不然，还确定一类拟阵及其中极值拟阵自由积为极值的充分条件。
中文摘要 AI 辅助
极值拟阵是那些在拟阵多面体中产生顶点的拟阵。我们展示了如何从拟阵\(M\)和\(M'\)在其拟阵多面体中的点，得到拟阵自由积\(M\square M'\)在适当拟阵多面体中的点。由此表明若\(M\square M'\)是极值的，则\(M\)和\(M'\)是极值的，反之不成立。我们确定了一大类包含完美拟阵设计和稀疏铺砌拟阵的拟阵，并找到了该类中极值拟阵自由积为极值的充分条件。
英文摘要
Extremal matroids are those that yield vertices in the polytope of matroids. We show how to get the point, in the appropriate polytope of matroids, for the free product $M\square M'$ of matroids $M$ and $M'$ from the points for $M$ and $M'$ in their polytopes of matroids. With this we show that if $M\square M'$ is extremal, then $M$ and $M'$ are extremal. The converse is false. We identify a large class of matroids that includes perfect matroid designs and sparse paving matroids, and we find sufficient conditions under which free products of extremal matroids in this class are extremal.
