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Differential equations for colored maps

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Random Geometry

Coauthor: Mireille Bousquet-Melou (CNRS)

We study the Potts model on planar maps. The partition function of this model is the generating function of colored maps counted according to the number of monochromatic edges and dichromatic edges. We characterize this partition function by a simple system of differential equations. Some special cases, such as properly 4-colored maps, have particularly simple equations waiting for a more direct combinatorial explanation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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