Recursive Generation of k-ary Trees
نویسنده
چکیده
In this paper we present a construction of every k-ary tree using a forest of (k− 1)ary trees satisfying a particular condition. We use this method recursively for the construction of the set of k-ary trees from the set of (k−1)-Dyck paths, thus obtaining a new bijection φ between these two sets. Furthermore, we introduce a new order on [k]∗ which is used for the full description of this bijection. Finally, we study some new statistics on k-ary trees which are transferred by φ to statistics concerning the occurrence of strings in (k − 1)-Dyck paths.
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