Rauzy, Gérard Nombres algébriques et substitutions. (French) Zbl 0522.10032 Bull. Soc. Math. Fr. 110, 147-178 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 13 ReviewsCited in 178 Documents MSC: 11K06 General theory of distribution modulo \(1\) 11A63 Radix representation; digital problems 11J71 Distribution modulo one Keywords:distribution modulo one; substitution; number system; two-dimensional analogue × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML Online Encyclopedia of Integer Sequences: Tribonacci word: limit S(infinity), where S(0) = 0, S(1) = 0,1, S(2) = 0,1,0,2 and for n >= 0, S(n+3) = S(n+2) S(n+1) S(n). The ternary tribonacci word; also a Rauzy fractal sequence: fixed point of the morphism 1 -> 12, 2 -> 13, 3 -> 1, starting from a(1) = 1. Apply the tribonacci morphism 1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1} n times to 1, and concatenate the resulting string. 0-limiting word of the morphism 0->10, 1->20, 2->0. Arnoux-Rauzy word sigma_0 x sigma_2 x sigma_1. Fixed point of the morphism 0-> 0201020, 1->1020, 2->201020 starting from a(1)=0. References: [1] ARTIN (E.) . - Theory of algebraic numbers , Göttingen, 1959 . MR 24 #A1884 | Zbl 0115.03503 · Zbl 0115.03503 [2] CHRISTOL (G.) , KAMAE (T.) , MENDÈS-FRANCE (M.) et RAUZY (G.) . - Suites algébriques , automates et substitutions, Bull. Soc. Math. Fr., 108, 1980 , p. 401-419. Numdam | MR 82e:10092 | Zbl 0472.10035 · Zbl 0472.10035 [3] DEKKING (M.) , MICHEL (P.) et KEANE (M.) . - Séminaire sur les substitutions , Rennes, 1977 . [4] RAUZY (G.) . - Une généralisation du développement en fraction continue , Séminaire Delonge-Pisot-Poitou, 1976 - 1977 . Numdam | Zbl 0369.28015 · Zbl 0369.28015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.