Powers in a class of A-strict standard episturmian words

Abstract

This paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic Sturmian words. In particular, we explicitly determine all integer powers occurring in such infinite words, extending recent results of Damanik and Lenz (2003), who studied powers in Sturmian words. The key tools in our analysis are canonical decompositions and a generalization of singular words, which were originally defined for the ubiquitous Fibonacci word. Our main results are demonstrated via some examples, including the $k$-bonacci word: a generalization of the Fibonacci word to a $k$-letter alphabet ($k\ge 2$).

26 pages; extended version of a paper presented at the 5th International Conference on Words, Montreal, Canada, September 13-17, 2005

References in corpus (2)

• Occurrences of palindromes in characteristic Sturmian words
• Conjugates of characteristic Sturmian words generated by morphisms

Cited by in corpus (5)

• Episturmian words: a survey
• Characterizations of finite and infinite episturmian words via lexicographic orderings
• A characterization of fine words over a finite alphabet
• Initial nonrepetitive complexity of regular episturmian words and their Diophantine exponents
• On a generalization of Christoffel words: epichristoffel words