Partial chord diagrams and matrix models
Partial chord diagrams and matrix models
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发表时间：
2016-12
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通讯作者：
J. Andersen;H. Fuji;Masahide Manabe;R. Penner;P. Sułkowski
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作者：
J. Andersen;H. Fuji;Masahide Manabe;R. Penner;P. Sułkowski
本文利用矩阵模型技术讨论了部分弦图的计数问题。除了骨架和弦数等基本数据外，我们还考虑了欧拉特征线、骨架谱、边界点谱和边界长度谱。此外，我们考虑的边界长度和点谱，统一后两种类型的谱。我们引入矩阵模型，编码生成函数的部分弦图过滤这些频谱。使用这些矩阵模型，我们推导出偏微分方程-获得独立的切割和加入参数在早期的工作-相应的生成函数。
In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations - obtained independently by cut-and-join arguments in an earlier work - for the corresponding generating functions.