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• W1551330783 endingPage "184" @default.
• W1551330783 startingPage "167" @default.
• W1551330783 abstract "We investigate a class of minimal sequences on a finite alphabet Ak = {1,2,...,k} having (k - 1)n + 1 distinct subwords of length n. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of binary Sturmian sequences. We describe two simple combinatorial algorithms for constructing characteristic Arnoux-Rauzy sequences (one of which is new even in the Sturmian case). Arnoux-Rauzy sequences arising from fixed points of primitive morphisms are characterized by an underlying periodic structure. We show that every Arnoux-Rauzy sequence contains arbitrarily large subwords of the form V^2+e and, in the Sturmian case, arbitrarily large subwords of the form V^3+e. Finally, we prove that an irrational number whose base b-digit expansion is an Arnoux-Rauzy sequence is transcendental." @default.
• W1551330783 created "2016-06-24" @default.
• W1551330783 creator A5024628248 @default.
• W1551330783 creator A5058663244 @default.
• W1551330783 date "2000-01-01" @default.
• W1551330783 modified "2023-09-29" @default.
• W1551330783 title "A generalization of Sturmian sequences: Combinatorial structure and transcendence" @default.
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• W1551330783 doi "https://doi.org/10.4064/aa-95-2-167-184" @default.
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