Enumerations of vertices among all rooted ordered trees with levels and degrees

Sen-Peng Eu, Seunghyun Seo, Heesung Shin

Research output: Contribution to journalArticle

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2123-2129
Number of pages7
JournalDiscrete Mathematics
Issue number9
Publication statusPublished - 2017 Sep 1



  • Degree
  • Enumeration
  • Level
  • Rooted ordered tree

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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