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A Combinatorial Approach to Positional Number Systems (1205.6460v2)

Published 29 May 2012 in math.CO, cs.DM, and math.NT

Abstract: Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits 0 and 1. Our combinatorial approach is to construct infinitely many binary radix systems, each one from a single pair of binary strings. Every binary radix system that satisfies even a minimal set of conditions that would be expected of a positional number system can be constructed in this way.

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