Department of Mathematics, FNSPE, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czech Republic; email@example.com
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.
(Received May 1 2004)
(Accepted June 8 2005)
(Online publication July 18 2007)
Mathematics Subject Classification: