Université Paris 8

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20022013

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math.NT2011★ 1 cited

Parallel addition in non-standard numeration systems

Christiane Frougny, Edita Pelantová, Milena Svobodová

We consider numeration systems where digits are integers and the base is an algebraic number $β$ such that $∣ β ∣ > 1$ and $β$ satisfies a polynomial where one coefficient is dominant…

math.NT2006★ 20 cited

On univoque Pisot numbers

J. -P. Allouche, C. Frougny, K. G. Hare

We study Pisot numbers $β \in (1, 2)$ which are univoque, i.e., such that there exists only one representation of 1 as $1 = \sum_{n \geq 1} s_{n} β^{- n}$ , with $s_{n} \in {0, 1}$ . We p…