Minoration of the complexity function associated to a translation on the torus
classification
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math.CO
keywords
translationcomplexityfunctiontorusassociatedconjugatedeveryinteger
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We show that the complexity function $p_k(n)$ of a piecewise translation map conjugated to a minimal translation on the torus $\TT^k = \RR^k / \ZZ^k$ is at least $kn+1$ for every integer $n$.
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