论文标题
石墨烯纳米酮和帕斯卡矩阵
Graphene nanocones and Pascal matrices
论文作者
论文摘要
我猜想了用Bloch（和更通用的）边界条件的石墨烯三角形和梯性的邻接矩阵决定因素的三个身份。对于三角形，参数决定因素等于对称Pascal基质的特征多项式。对于梯形，它等于子矩阵的决定因素。最后，紧密结合基质的决定因素等于其永久性。对中等大小的分析评估和Mathematica支持了这些猜想。他们建立了与分区的计数问题，六角形的块状砖块，圆柱上密集的循环的联系。
I conjecture three identities for the determinant of adjacency matrices of graphene triangles and trapezia with Bloch (and more general) boundary conditions. For triangles, the parametric determinant is equal to the characteristic polynomial of the symmetric Pascal matrix. For trapezia it is equal to the determinant of a sub-matrix. Finally, the determinant of the tight binding matrix equals its permanent. The conjectures are supported by analytic evaluations and Mathematica, for moderate sizes. They establish connections with counting problems of partitions, lozenge tilings of hexagons, dense loops on a cylinder.
