A characterization of Sturmian sequences by indistinguishable asymptotic pairs

@article{Barbieri2021ACO,
  title={A characterization of Sturmian sequences by indistinguishable asymptotic pairs},
  author={Sebastiano Barbieri and S{\'e}bastien Labb{\'e} and {\vS}těp{\'a}n Starosta},
  journal={Eur. J. Comb.},
  year={2021},
  volume={95},
  pages={103318}
}
View PDF on arXiv
2 Citations
Background Citations
1
Methods Citations
1
Results Citations
1

Figures from this paper

2 Citations

Indistinguishable asymptotic pairs and multidimensional Sturmian configurations
. Two asymptotic configurations on a full Z d -shift are indistinguishable if for every finite pattern the associated sets of occurrences in each configuration coincide up to a finitely supported…
The $q$-analog of the Markoff injectivity conjecture over the language of a balanced sequence
The Markoff injectivity conjecture states that w 7→ μ(w)12 is injective on the set of Christoffel words where μ : {0, 1}∗ → SL2(Z) is a certain homomorphism and M12 is the entry above the diagonal of…

References

SHOWING 1-10 OF 31 REFERENCES
Some Combinatorial Properties of Sturmian Words
Recent Results on Extensions of Sturmian Words
TLDR
In this survey, combinatorial properties of these two families are considered and compared and the Arnoux–Rauzy words appear to share many of the properties of Sturmian words.
A curious characteristic property of standard Sturmian words
Sturmian words have been studied for a very long time (Bernoulli [1], Christoffel [3], Markoff [18], Morse and Hedlund [19], Coven and Hedlund [5], Lunnon and Pleasants [17],…). They are infinite…
Sturmian Words, Lyndon Words and Trees
Sturmian and episturmian words: a survey of some recent results
This survey paper contains a description of some recent results concerning Sturmian and episturmian words, with particular emphasis on central words. We list fourteen characterizations of central…
Gibbsian Representations of Continuous Specifications: The Theorems of Kozlov and Sullivan Revisited
The theorems of Kozlov and Sullivan characterize Gibbs measures as measures with positive continuous specifications. More precisely, Kozlov showed that every positive continuous specification on…
0-1-sequences of Toeplitz type
Summary0-1-sequences are constructed by successive insertion of a periodic sequence of symbols 0, 1 and “hole” into the “holes” of the sequence already constructed. Assuming that finally all “holes”…
Palindromic richness
Sequences with minimal block growth II
  • E. Coven
  • Mathematics
    Mathematical systems theory
  • 2005
TLDR
The class of sequences with minimal block growth is closed under flow isomorphism and contains all sequences x satisfying P(x, n) = n + 1 for all n _> 1.
A characterization of substitutive sequences using return words
  • F. Durand
  • Economics, Philosophy
    Discret. Math.
  • 1998
...
...