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**1 - 1**of**1**### Admissible Digit Sets and a Modified Stern-Brocot Representation

, 2004

"... We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a nite number of Mobius transformations. We regard certain sets of Mobius transformations as a generalized notion of digits and introduce sucient conditions that such a \digit ..."

Abstract
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We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a nite number of Mobius transformations. We regard certain sets of Mobius transformations as a generalized notion of digits and introduce sucient conditions that such a \digit set" yields an admissible representation of [0; +1]. Furthermore we establish the productivity and correctness of the homographic algorithm for such \admissible" digit sets. In the second part of the paper we discuss representation of positive real numbers based on the Stern{Brocot tree. We show how we can modify the usual Stern{Brocot representation to yield a ternary admissible digit set.