Abstract
Let n denote the set of trees on n labeled vertices. In this paper, we consider the statistic on n which records the number of vertices of odd degree and count trees having a prescribed number of such vertices. In doing so, we make use of a well-known bijection between members of n and the set of n-ary words of length n-2. In fact, we are able to study a generalization mod r of the aforementioned statistic for all r ≥ 2. In the cases when r = 2 and r = 3, further enumerative results for both words and trees may be given.
Original language | English |
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Article number | 1650031 |
Journal | Discrete Mathematics, Algorithms and Applications |
Volume | 8 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jun 2016 |
Bibliographical note
Publisher Copyright:© 2016 World Scientific Publishing Company.
Keywords
- Prüfer code
- generating function
- k-ary words
- trees
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics