Balance properties of the fixed point of the substitution associated to quadratic simple Pisot numbers
Department of Mathematics, FNSPE, Czech Technical University,
Trojanova 13, 120 00 Praha 2, Czech Republic; firstname.lastname@example.org
Accepted: 8 June 2005
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 , for , , , where . We will prove that such word is t-balanced with . 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 , is not m-balanced for any m. We exhibit an infinite sequence of pairs of words with the unbalance property.
Mathematics Subject Classification: 68R15
Key words: Balance property / substitution invariant / Parry number
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