论文标题
HyperGraph矩阵模型和生成功能
Hypergraph matrix models and generating functions
论文作者
论文摘要
最近，我们引入了HyperGraph矩阵模型（HMM），这是一种遗传基质模型，概括了经典的高斯单位合奏（GUE）。在这个模型中，Gue的高斯人的瞬间计数有限的分区被设置为对的，被正式措施所取代，其矩数将分区设置为固定均匀尺寸的2m> = 2的部分。就像对痕量多项式的期望Tr x^{2r}在gue中产生多种态度的单次相同的象征，这些杂物可产生不同的象征，这些象征的象征性均匀的象征，这些象征的象征性斑点均为多个象征，这些象征的象征斑点均为多个象征，这些象征的象征均匀斑点均为象征。用指令来计算某些Unicelled Edge-ramified CW复合物，并使用指令来调用（定向CW）地图。在本文中，我们描述了用固定属的说明以及任意顶点的指令生成地图的生成功能。我们的结果是由赖特（Wright）的工作激励。特别地，赖特计算的固定第一个betti编号连接的图形的生成函数是根函数t（x）中的有理函数，作为功能关系的解决方案x = t e^{ - t}的解决方案。
Recently we introduced the hypergraph matrix model (HMM), a Hermitian matrix model generalizing the classical Gaussian Unitary Ensemble (GUE). In this model the Gaussians of the GUE, whose moments count partitions of finite sets into pairs, are replaced by formal measures whose moments count set partitions into parts of a fixed even size 2m >= 2. Just as the expectations of the trace polynomials Tr X^{2r} in the GUE produce polynomials counting unicellular orientable maps of different genera, in the HHM these expectations give polynomials counting certain unicelled edge-ramified CW complexes with extra data that we call (orientable CW) maps with instructions. In this paper we describe generating functions for maps with instructions of fixed genus and with the number of vertices arbitrary. Our results are motivated by work of Wright. In particular Wright computed generating functions of connected graphs of fixed first Betti number as rational functions in the rooted tree function T (x), given as the solution to the functional relation x = T e^{-T}.
