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.
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- Prüfer code
- generating function
- k-ary words
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics