bijections for classes of labelled trees

Trees are acyclic connected graphs. plane trees, d-ary trees, binary trees, noncrossingtrees and their generalizations, which are families of trees, have been enumerated bymany authors using various statistics. these trees are known to be enumerated by catalan orcatalan-like formulas (fuss-catalan numbers). one of the most common approaches to theenumeration of these trees is by means of generating functions. another method that can beused to enumerate them is by constructing bijections between sets of the same cardinality. thebijective method is preferred to other methods by many combinatorialists. so, in this paper, weconstruct bijections relating k-plane trees, k-noncrossing increasing trees, k-noncrossing trees,k-binary trees and weakly labelled k-trees.