Pisot Numbers and Greedy Algorithm
نویسندگان
چکیده
منابع مشابه
Beta Expansions for Regular Pisot Numbers
A beta expansion is the analogue of the base 10 representation of a real number, where the base may be a non-integer. Although the greedy beta expansion of 1 using a non-integer base is, in general, infinitely long and non-repeating, it is known that if the base is a Pisot number, then this expansion will always be finite or periodic. Some work has been done to learn more about these expansions...
متن کاملBeta-expansions, natural extensions and multiple tilings associated with Pisot units
From the works of Rauzy and Thurston, we know how to construct (multiple) tilings of some Euclidean space using the conjugates of a Pisot unit β and the greedy β-transformation. In this paper, we consider different transformations generating expansions in base β, including cases where the associated subshift is not sofic. Under certain mild conditions, we show that they give multiple tilings. W...
متن کاملBeta-expansions, Natural Extensions and Multiple Tilings
From the works of Rauzy and Thurston, we know how to construct (multiple) tilings of some Euclidean space using the conjugates of a Pisot unit β and the greedy β-transformation. In this paper, we consider different transformations generating expansions in base β. Under certain mild conditions, we show that they give multiple tilings. We also give a necessary and sufficient condition for the til...
متن کاملSome computations on the spectra of Pisot and Salem numbers
Properties of Pisot numbers have long been of interest. One line of questioning, initiated by Erdős, Joó and Komornik in 1990, is the determination of l(q) for Pisot numbers q, where l(q) = inf(|y| : y = 0 + 1q + · · ·+ nq, i ∈ {±1, 0}, y 6= 0). Although the quantity l(q) is known for some Pisot numbers q, there has been no general method for computing l(q). This paper gives such an algorithm. ...
متن کاملOn certain computations of Pisot numbers
This paper presents two algorithms on certain computations about Pisot numbers. Firstly, we develop an algorithm that finds a Pisot number α such that Q[α] = F given a real Galois extension F of Q by its integral basis. This algorithm is based on the lattice reduction, and it runs in time polynomial in the size of the integral basis. Next, we show that for a fixed Pisot number α, one can comput...
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تاریخ انتشار 1996