Matrix model combinatorics: applications to folding and coloring
Matrix model combinatorics: applications to folding and coloring
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矩阵模型组合学：在折叠和着色中的应用
DOI：
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发表时间：
1999
期刊：
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通讯作者：
P. Francesco
中科院分区：
文献类型：
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作者：
P. Francesco
我们详细研究了矩阵积分的组合解释，包括任意属的镶嵌和随机表面上的循环模型的例子。在回顾了他们的解决方法后，我们将其应用于研究物理学中的各种折叠问题，包括：弯折（或聚合物折叠）问题“所有拓扑不等价的与通过给定数量点的线相交的闭合非相交平面曲线的枚举”和流体膜折叠问题，其被重新表述为“枚举任意亏格的所有顶点三色三角剖分”，其中任一颜色的顶点的数量给定“。
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these to the study of various folding problems arising from physics, including: the meander (or polymer folding) problem ``enumeration of all topologically inequivalent closed non-intersecting plane curves intersecting a line through a given number of points" and a fluid membrane folding problem reformulated as that of ``enumerating all vertex-tricolored triangulations of arbitrary genus, with given numbers of vertices of either color".