Powers in a class of A-strict standard episturmian words

  • Authors:

  • Amy Glen

  • Affiliations:

  • LaCIM, Université du Québec à Montréal, C.P. 8888, Succ. Centre-ville, Montréal, Québec, Canada, H3C 3P8

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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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 [D. Damanik, D. Lenz, Powers in Sturmian sequences, European J. Combin. 24 (2003) 377-390, doi:10.1016/S0195-6698(03)00026-X], 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=2).