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- W2117524189 abstract "We study α-adic expansions of numbers, that is to say, left infinite representations of numbers in the positional numeration system with the base α, where α is an algebraic conjugate of a Pisot number β. Based on a result of Bertrand and Schmidt, we prove that a number belongs to Q(α) if and only if it has an eventually periodic α-adic expansion. Then we consider α-adic expansions of elements of the ring Z[α−1] when β satisfies the so-called Finiteness property (F). We give two algorithms for computing these expansions — one for positive and one for negative numbers. In the particular case that β is a quadratic Pisot unit satisfying (F), we inspect the unicity and/or multiplicity of α-adic expansions of elements of Z[α−1]. We also provide algorithms to generate α-adic expansions of rational numbers in that case." @default.
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- W2117524189 date "2007-06-01" @default.
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- W2117524189 title "On alpha-adic expansions in Pisot bases" @default.
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- W2117524189 doi "https://doi.org/10.1016/j.tcs.2007.03.018" @default.
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