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Une propriété de domination convexe pour les orbites sturmiennes
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- Journal:
- Canadian Journal of Mathematics / Volume 67 / Issue 1 / 01 February 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 90-106
- Print publication:
- 01 February 2015
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- Article
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Let
$\mathbf{x}\,=\,\left( {{x}_{0}},\,{{x}_{1}},.\,.\,. \right)$ be a 
$N$-periodic sequence of integers 
$\left( N\,\ge \,1 \right)$, and 
$\mathbf{s}$ a sturmian sequence with the same barycenter (and also $N$-periodic, consequently). It is shown that, for affine functions 
$\alpha :\,\mathbb{R}_{(N)}^{\mathbb{N}}\,\to \,\mathbb{R}$ which are increasing relatively to some order 
${{\le }_{2}}$ on 
$\mathbb{R}_{(N)}^{\mathbb{R}}$ (the space of all $N$-periodic sequences), the average of 
$\left| \alpha \right|$ on the orbit of 
$\mathbf{x}$ is greater than its average on the orbit of $\mathbf{s}$.
