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Minimal expansions in redundant number systems: Fibonacci bases and Greedy algorithms

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Abstract

We study digit expansions with arbitrary integer digits in base q (q integer) and the Fibonacci base such that the sum of the absolute values of the digits is minimal. For the Fibonacci case, we describe a unique minimal expansion and give a greedy algorithm to compute it. Additionally, transducers to calculate minimal expansions from other expansions are given. For the case of even integer bases q, similar results are given which complement those given in [6].

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  1. Institut für Mathematik B, Technische Universität Graz Steyrergasse 30, A-8010, Graz, Austria

    Clemens Heuberger

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  1. Clemens Heuberger
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Heuberger, C. Minimal expansions in redundant number systems: Fibonacci bases and Greedy algorithms. Period Math Hung 49, 65–89 (2004). https://doi.org/10.1007/s10998-004-0523-x

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