Displaying similar documents to “Palindromic complexity of infinite words associated with simple Parry numbers”

Substitutions with Cofinal Fixed Points

Bo TAN, Zhi-Xiong WEN, Jun WU, Zhi-Ying WEN (2006)

Annales de l’institut Fourier

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Let ϕ be a substitution over a 2-letter alphabet, say { a , b } . If ϕ ( a ) and ϕ ( b ) begin with a and b respectively, ϕ has two fixed points beginning with a and b respectively. We characterize substitutions with two cofinal fixed points (i.e., which differ only by prefixes). The proof is a combinatorial one, based on the study of repetitions of words in the fixed points.

Substitutions, abstract number systems and the space filling property

Clemens Fuchs, Robert Tijdeman (2006)

Annales de l’institut Fourier

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In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo 1 and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.

Words and repeated factors.

Carpi, Arturo, de Luca, Aldo (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

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A Characterization of Multidimensional S -Automatic Sequences

Emilie Charlier, Tomi Kärki, Michel Rigo (2009)

Actes des rencontres du CIRM

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An infinite word is S -automatic if, for all n ≥ 0 , its ( n + 1 ) st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S . In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d ≥ 2 , we state that a multidimensional infinite word x : ℕ d → Σ over a finite alphabet Σ is S -automatic for some abstract...

Substitutions on two letters, cutting segments and their projections

Sierk W. Rosema (2007)

Journal de Théorie des Nombres de Bordeaux

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In this paper we study the structure of the projections of the finite cutting segments corresponding to unimodular substitutions over a two-letter alphabet. We show that such a projection is a block of letters if and only if the substitution is Sturmian. Applying the procedure of projecting the cutting segments corresponding to a Christoffel substitution twice results in the original substitution. This induces a duality on the set of Christoffel substitutions.

Generalized Thue-Morse words and palindromic richness

Štěpán Starosta (2012)

Kybernetika

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We prove that the generalized Thue-Morse word 𝐭 b , m defined for b ≥ 2 and m ≥ 1 as 𝐭 b , m = s b ( n ) mod m n = 0 + ∞ , where s b ( n ) denotes the sum of digits in the base- b representation of the integer n , has its language closed under all elements of a group D m isomorphic to the dihedral group of order 2 m consisting of morphisms and antimorphisms. Considering antimorphisms Θ ∈ D m , we show that 𝐭 b , m is saturated by Θ -palindromes up to the highest possible level. Using the generalisation of palindromic richness recently introduced by the author...