Abstract
The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers β having the negative finiteness property, that is the set of finite (−β)-expansions is equal to \({\mathbb{Z}[\beta^{-1}]}\). For a class of numbers including the Tribonacci number, we compute the maximal length of the fractional parts arising in the addition and subtraction of (−β)-integers. We also give conditions excluding the negative finiteness property.
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