Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 123-135.

In this paper we will deal with the balance properties of the infinite binary words associated to β-integers when β is a quadratic simple Pisot number. Those words are the fixed points of the morphisms of the type ϕ(A)=A p B, ϕ(B)=A q for p, q, pq, where β=p+p 2 +4q 2. We will prove that such word is t-balanced with t=1+(p-1)/(p+1-q). Finally, in the case that p<q it is known [B. Adamczewski, Theoret. Comput. Sci. 273 (2002) 197-224] that the fixed point of the substitution ϕ(A)=A p B, ϕ(B)=A q is not m-balanced for any m. We exhibit an infinite sequence of pairs of words with the unbalance property.

DOI : https://doi.org/10.1051/ita:2007009
Classification : 68R15
Mots clés : balance property, substitution invariant, Parry number
@article{ITA_2007__41_2_123_0,
     author = {Turek, Ond\v{r}ej},
     title = {Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {123--135},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {2},
     year = {2007},
     doi = {10.1051/ita:2007009},
     mrnumber = {2350639},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2007009/}
}
Turek, Ondřej. Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 2, pp. 123-135. doi : 10.1051/ita:2007009. http://archive.numdam.org/articles/10.1051/ita:2007009/

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