Admissible digit sets

We examine a special case of admissible representations of the closed interval, namely those which arise via sequences of a finite number of Mobius transformations. We regard certain sets of Mobius transformations as a generalized notion of digits and introduce sufficient conditions that such a "digit set" yields an admissible representation of [0, +infinity]. Furthermore, we establish the productivity and correctness of the homographic algorithm for such "admissible" digit sets. We present the Stem-Brocot representation and a modification of same as a working example throughout. (c) 2005 Elsevier B.V. All rights reserved.