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Differential equations for colored maps

Presented by: 
O Bernardi Brandeis University
Date: 
Wednesday 22nd April 2015 - 14:00 to 15:00
Venue: 
INI Seminar Room 1
Abstract: 
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.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons