4 research outputs found
Finite beta-expansions with negative bases
The finiteness property is an important arithmetical property of
beta-expansions. We exhibit classes of Pisot numbers having the
negative finiteness property, that is the set of finite -expansions
is equal to . 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 -integers. We also give
conditions excluding the negative finiteness property