论文标题
晶格路径双子曲霉
Lattice path bicircular matroids
论文作者
论文摘要
晶格路径矩形和双子曲霉是两种众所周知的横向曲霉类。在Bonin和de Mier关于晶格路径矩形的结构特性的开创性工作中，作者声称晶格路径矩阵与双圆形矩阵明显不同。最近，证明所有cosimple晶状体原子体具有正双回路，而表明有一大类Cosimple双子曲霉，没有正双电路。这些观察结果支持Bonin和De Miers的主张。最后，Sivaraman和Slilaty建议研究晶格路径矩形和双圆形曲霉的交集，这可能是一个有趣的研究主题。在这项工作中，我们展示了用于晶格路径矩阵类别的排除双子曲霉，并提出了图族的特征，其双子矩阵是晶格路径矩阵。作为这种表征的应用，我们提出了$ 2 $连接的晶格双子矩阵的几何描述。
Lattice path matroids and bicircular matroids are two well-known classes of transversal matroids. In the seminal work of Bonin and de Mier about structural properties of lattice path matroids, the authors claimed that lattice path matroids significantly differ from bicircular matroids. Recently, it was proved that all cosimple lattice path matroids have positive double circuits, while it was shown that there is a large class of cosimple bicircular matroids with no positive double circuits. These observations support Bonin and de Miers' claim. Finally, Sivaraman and Slilaty suggested studying the intersection of lattice path matroids and bicircular matroids as a possibly interesting research topic. In this work, we exhibit the excluded bicircular matroids for the class of lattice path matroids, and we propose a characterization of the graph family whose bicircular matroids are lattice path matroids. As an application of this characterization, we propose a geometric description of $2$-connected lattice path bicircular matroids.
