Powers in a class of A-strict standard episturmian words

Details Powers in a class of A-strict standard episturmian words Powers in a class of A-strict standard episturmian words

2007-08-31

arxiv.org/abs/0708.4400v1

Theoretical Computer Science 380 (2007) 330-354

Mathematics

Combinatorics

26 pages; extended version of a paper presented at the 5th International Conference on Words, Montreal, Canada, September 13-1

Scientific paper

10.1016/j.tcs.2007.03.023

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 ($k\geq2$).

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