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• W4378220280 abstract "Let θ=[0;a 1 ,a 2 ,⋯] be the continued fraction expansion of an irrational real number θ∈(0,1). It is well-known that the characteristic Sturmian word of slope θ is the limit of a sequence of finite words (M k ) k≥0 , with M k of length q k (the denominator of the k-th convergent to θ) being a suitable concatenation of a k copies of M k-1 and one copy of M k-2 . Our first result extends this to any Sturmian word s. Let b≥2 be an integer. Our second result gives the continued fraction expansion of any real number ξ whose b-ary expansion is a Sturmian word s over the alphabet {0,b-1}. This extends a classical result of Böhmer who considered only the case where s is characteristic. As a consequence, we obtain a formula for the irrationality exponent of ξ in terms of the slope and the intercept of s." @default.
• W4378220280 created "2023-05-26" @default.
• W4378220280 creator A5087094437 @default.
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• W4378220280 date "2023-10-09" @default.
• W4378220280 modified "2023-10-10" @default.
• W4378220280 title "Combinatorial structure of Sturmian words and continued fraction expansion of Sturmian numbers" @default.
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• W4378220280 doi "https://doi.org/10.5802/aif.3561" @default.
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