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Combinatorial and probabilistic properties of systems of numeration
Published online by Cambridge University Press: 16 September 2014
Abstract
Let $G=(G_{n})_{n}$ be a strictly increasing sequence of positive integers with
$G_{0}=1$. We study the system of numeration defined by this sequence by looking at the corresponding compactification
${\mathcal{K}}_{G}$ of
$\mathbb{N}$ and the extension of the addition-by-one map
${\it\tau}$ on
${\mathcal{K}}_{G}$ (the ‘odometer’). We give sufficient conditions for the existence and uniqueness of
${\it\tau}$-invariant measures on
${\mathcal{K}}_{G}$ in terms of combinatorial properties of
$G$.
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- Research Article
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- © Cambridge University Press, 2014
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