Abstract
Smooth infinite words over Σ = { 1 , 2 } are connected to the Kolakoski word K = 221121 ⋯ , defined as the fixpoint of the function Δ that counts the length of the runs of 1's and 2's. In this paper we extend the notion of smooth words to arbitrary alphabets and study some of their combinatorial properties. Using the run-length encoding Δ , every word is represented by a word obtained from the iterations of Δ . In particular we provide a new representation of the infinite Fibonacci word F as an eventually periodic word. On the other hand, the Thue–Morse word is represented by a finite one.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
