In this paper we enumerate and give bijections for the following four sets of vertices among rooted ordered trees of a fixed size: (i) first-children of degree k at level ℓ, (ii) non-first-children of degree k at level ℓ−1, (iii) leaves having k−1 elder siblings at level ℓ, and (iv) non-leaves of outdegree k at level ℓ−1. Our results unite and generalize several previous works in the literature.
- Rooted ordered tree
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics