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Planar Maps as Labeled Mobiles
2004
Electronic Journal of Combinatorics
We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to the general case of Eulerian planar maps with prescribed face valences to obtain a bijection with a new class of labeled trees, which we call mobiles. Our bijection covers all the classes of maps previously enumerated by either the two-matrix model used by physicists or by the bijection with blossom trees used by combinatorists. Our bijection reduces the enumeration of maps to that, much simpler, of
doi:10.37236/1822
fatcat:5qllntsep5dv5geurhqrc5ijv4