| Issue |
RAIRO-Theor. Inf. Appl.
Volume 41, Number 2, April-June 2007
|
|
|---|---|---|
| Page(s) | 123 - 135 | |
| DOI | https://doi.org/10.1051/ita:2007009 | |
| Published online | 18 July 2007 | |
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; oturek@centrum.cz
Received:
1
May
2004
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 ![$t=1+\left[(p-1)/(p+1-q)\right]$](/articles/ita/abs/2007/02/ita05012/ita05012_tex_eq7.png)
. 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
© EDP Sciences, 2007
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