Enumeration of r-smooth words over a finite alphabet

Toufik Mansour, José L. Ramírez, Diego Villamizar

Research output: Contribution to journalArticlepeer-review


In this paper, we enumerate a restricted family of k-ary words called r-smooth words. The restriction is defined through the distance between adjacent changes in the word. Using automata, we enumerate this family of words. Additionally, we give explicit combinatorial expressions to enumerate the words and asymptotic expansions related to the Fibonacci sequence.

Original languageEnglish
Pages (from-to)68-75
Number of pages8
JournalDiscrete Mathematics Letters
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 the authors.


  • automata
  • generating function
  • k-ary word

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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