On repetition-free binary words of minimal density
Identifieur interne : 00B162 ( Main/Merge ); précédent : 00B161; suivant : 00B163On repetition-free binary words of minimal density
Auteurs : R. Kolpakov [Russie] ; G. Kucherov [France] ; Y. Tarannikov [Russie]Source :
- Theoretical computer science [ 0304-3975 ] ; 1999.
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- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
We study the minimal proportion (density) of one letter in nth power-free binary words. First, we introduce and analyse a general notion of minimal letter density for any infinite set of words which does not contain a specified set of "prohibited" subwords. We then prove that for nth power-free binary words the density function is 1/n + 1/n3+ 1/n4 + O(1/n5). We also consider a generalization of nth power-free words for fractional powers (exponents): a word is xth power-free for a real x, if it does not contain subwords of exponent x or more. We study the minimal proportion of one letter in xth power-free binary words as a function of x and prove, in particular, that this function is discontinuous at 7/3 as well as at all integer points n ≥ 3. Finally, we give an estimate of the size of the jumps.
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Pascal:99-0409404Le document en format XML
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<front><div type="abstract" xml:lang="en">We study the minimal proportion (density) of one letter in nth power-free binary words. First, we introduce and analyse a general notion of minimal letter density for any infinite set of words which does not contain a specified set of "prohibited" subwords. We then prove that for nth power-free binary words the density function is 1/n + 1/n<sup>3</sup>
+ 1/n<sup>4</sup>
+ O(1/n<sup>5</sup>
). We also consider a generalization of nth power-free words for fractional powers (exponents): a word is xth power-free for a real x, if it does not contain subwords of exponent x or more. We study the minimal proportion of one letter in xth power-free binary words as a function of x and prove, in particular, that this function is discontinuous at 7/3 as well as at all integer points n ≥ 3. Finally, we give an estimate of the size of the jumps.</div>
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