论文标题
几何图的新生产矩阵
New production matrices for geometric graphs
论文作者
论文摘要
我们使用生产矩阵来计算几类几何图。我们提出了用于非交叉分区，连接的几何图和K-Gyaneles的新型生产矩阵，这些矩阵提供了另一种计算此类对象数量的方式。然后，计数几何图等效于计算生产矩阵的幂。将Riordan阵列的技术应用于这些生产矩阵，我们为几何图的数量以及从生产矩阵得出的组合身份建立了新公式。此外，我们获得了此类生产矩阵的特征多项式和特征向量。
We use production matrices to count several classes of geometric graphs. We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. Counting geometric graphs is then equivalent to calculating the powers of a production matrix. Applying the technique of Riordan Arrays to these production matrices, we establish new formulas for the numbers of geometric graphs as well as combinatorial identities derived from the production matrices. Further, we obtain the characteristic polynomial and the eigenvectors of such production matrices.
