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Recurrent word information


In mathematics, a recurrent word or sequence is an infinite word over a finite alphabet in which every factor occurs infinitely many times.[1][2][3] An infinite word is recurrent if and only if it is a sesquipower.[4][5]

A uniformly recurrent word is a recurrent word in which for any given factor X in the sequence, there is some length nX (often much longer than the length of X) such that X appears in every block of length nX.[1][6][7] The terms minimal sequence[8] and almost periodic sequence (Muchnik, Semenov, Ushakov 2003) are also used.

  1. ^ a b Lothaire (2011) p. 30
  2. ^ Allouche & Shallit (2003) p.325
  3. ^ Pytheas Fogg (2002) p.2
  4. ^ Lothaire (2011) p. 141
  5. ^ Berstel et al (2009) p.133
  6. ^ Berthé & Rigo (2010) p.7
  7. ^ Allouche & Shallit (2003) p.328
  8. ^ Pytheas Fogg (2002) p.6

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