Matrix Model Combinatorics: Applications to Folding and Coloring

Details Matrix Model Combinatorics: Applications to Folding and Coloring Matrix Model Combinatorics: Applications to Folding and Coloring

1999-11-02

arxiv.org/abs/math-ph/9911002v1

Physics

Mathematical Physics

69 pp, 24 figs, uses harvmac and epsf

Scientific paper

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".

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