On the Zero Defect Conjecture

@article{Labb2017OnTZ,
  title={On the Zero Defect Conjecture},
  author={S{\'e}bastien Labb{\'e} and Edita Pelantov{\'a} and {\vS}těp{\'a}n Starosta},
  journal={Eur. J. Comb.},
  year={2017},
  volume={62},
  pages={132-146}
}
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References

SHOWING 1-10 OF 31 REFERENCES
A Counterexample to a Question of Hof, Knill and Simon
TLDR
A negative answer is given to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite number of palindromes about the existence of a counterexample on the ternary alphabet.
On The Palindromic Complexity Of Infinite Words
TLDR
It is proved that there exist periodic words having the maximum number of palindromes as in the case of Sturmian words, by providing a simple and easy to check condition.
Combinatorial properties of f-palindromes in the Thue-Morse sequence ∗
The palindromic defect of a finite word w is defined as D(w) = |w|+ 1 − |Pal(w)| where Pal(w) is the set of its palindromic factors. In this paper we study the problem of computing the palindromic…
Palindromic sequences generated from marked morphisms
Proof of the Brlek-Reutenauer conjecture
Exchange of three intervals: Substitutions and palindromicity
A connection between palindromic and factor complexity using return words
Mirror substitutions and palindromic sequences
By introducing the notion of mirror substitution, we show that, given a substitutive sequence over two letters, it is palindromic (that is, it contains arbitrarily long palindromes) if and only if…
Exchange of three intervals: itineraries, substitutions and palindromicity
Given a symmetric exchange of three intervals, we provide a detailed description of the return times to a subinterval and the corresponding itineraries. We apply our results to morphisms fixing words…
Episturmian words and some constructions of de Luca and Rauzy
...
...