Zeckendorf Representations Using Negative Fibonacci Numbers

1992/05/01 by M. W. Bunder · 1 citation
Physics and Astronomy · #Advanced Mathematical Theories and Applications

paper · doi:10.1080/00150517.1992.12429361

Abstract

It is well known that every positive integer can be represented uniquely as a sum of distinct, nonconsecutive Fibonacci numbers (see, e.g., Brown [1]. This representation is called the Zeckendorf representation of the positive integer. Other Zeckendorf-type representations where the Fibonacci numbers are not necessarily consecutive are possible. Brown [2] considers one where a maximal number of distinct Fibonacci numbers are used rather than a minimal number.

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