n-Colored Maps and Multilabel n-Colored Trees
New topological operations are introduced in order to recover in another way the generalized Dyck equation for the generating function of n-colored maps presented in a former paper by decomposing maps topologically and bijectively. Applying repeatedly the operations which allowed to reveal the generalized Dyck equation to the successive transformed maps a one-to-one correspondence is obtained between n-colored maps on any surface and n-colored trees whose vertices can be labelled with several labels. This bijection provides us with coding of these maps.
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