Factors of Words

@inproceedings{Beauquier1989FactorsOW,
  title={Factors of Words},
  author={Dani{\`e}le Beauquier and Jean-{\'E}ric Pin},
  booktitle={ICALP},
  year={1989}
}
Let A be an alphabet of cardinality m, n k be a sequence of positive integers and ( ) n w A w k ∈ = . In this paper it is shown that if lim supn→ ∞ kn/ ln n < 1/ lnm then almost all words of length n over A contain the factor w, but if lim supn→ ∞ kn/ln n> 1/ lnm then this property is not true. Also, if lim infn→ ∞ kn/ lnn >1/ lnm then almost all words of length n over A do not contain the factor w. Moreover, if lim (ln ln ) n n n k m α → ∞ − = ∈ ¡ then limsup ( , , , / 1 exp( exp( )) n n n W n… CONTINUE READING

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