Smooth words over arbitrary alphabets
Smooth infinite words over Sigma = {1, 2} are connected to the Kolakoski word K = 221121 (...), defined as the fixpoint of the function Delta 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 Delta, every word is represented by a word obtained from the iterations of Delta. 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. (c) 2005 Elsevier B.V. All rights reserved.
smooth words kolakoski word run-length encoding fibonacci word thue-morse word sturmian words