Non-repetitive words: Ages and essences

Abstract

This paper introduces the notions of age and essence of an infinite wordw. Using these notions, the author studies the setL of infinite non-repetitive words over {1,2,3}, and its proper subsetsL 121,L 121,323,L 121,212, where words ofL 121 (L 121,323;L 121,212) do not contain 121 (121,323;121,212) as subwords. Motivated by the question ‘How many essentially different nonrepetitive words over {1,2,3} exist?’ the author counts the equivalence classes ofL,L 121,L 121,323,L 121,212 under agreement in a final segment, agreement in age, and in essence.

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This work was supported by an NSERC operating grant.

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Currie, J.D. Non-repetitive words: Ages and essences. Combinatorica 16, 19–40 (1996). https://doi.org/10.1007/BF01300125

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Mathematics Subject Classification (1991)

  • 68 Q
  • 03 C