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  • Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u)= sum_{n=0}^{+infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n)+2 - P_u(n)-P_u(n+1), where C_u(n) and P_u(n) are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words.
  • Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u)= sum_{n=0}^{+infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n)+2 - P_u(n)-P_u(n+1), where C_u(n) and P_u(n) are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words. (en)
Title
  • Proof of the Brlek-Reutenauer conjecture
  • Proof of the Brlek-Reutenauer conjecture (en)
skos:prefLabel
  • Proof of the Brlek-Reutenauer conjecture
  • Proof of the Brlek-Reutenauer conjecture (en)
skos:notation
  • RIV/68407700:21240/13:00201614!RIV14-MSM-21240___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/09/0584), S, Z(MSM6840770039)
http://linked.open...iv/cisloPeriodika
  • 0
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  • 100348
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21240/13:00201614
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  • defect; palindrome; complexity (en)
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [57C59ED60A88]
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  • Theoretical Computer Science
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  • 475
http://linked.open...iv/tvurceVysledku
  • Balková, Lubomíra
  • Pelantová, Edita
  • Starosta, Štěpán
http://linked.open...ain/vavai/riv/wos
  • 000315309600013
http://linked.open...n/vavai/riv/zamer
issn
  • 0304-3975
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.tcs.2012.12.024
http://localhost/t...ganizacniJednotka
  • 21240
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