A statistic related to trees and words on a finite alphabet

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number1650031
JournalDiscrete Mathematics, Algorithms and Applications
Issue number2
StatePublished - 1 Jun 2016

Bibliographical note

Publisher Copyright:
© 2016 World Scientific Publishing Company.


  • Prüfer code
  • generating function
  • k-ary words
  • trees

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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