Generalized Dyck equations and multilabel trees

New topological operations are introduced in order to recover in another way the generalized Dyck equations presented by D. Arquès and al. for the generating functions of maps and colored maps, by decomposing maps topologically and bijectively. Applying repeatedly the operations which made it possible to reveal the generalized Dyck equations for the successive transformed maps, one-to-one correspondences are obtained between maps (colored or not) of indeterminate genus and trees (colored or not) whose vertices can be labelled with several labels, following rules that we will define. These bijections provide us with a coding of these maps