Dumont-Thomas numeration systems for ℤ

Abstract: We extend the well-known Dumont-Thomas numeration system to ℤ by considering two-sided periodic points of a substitution, thus allowing us to represent any integer in ℤ by a finite word (starting with 0 when nonnegative and with 1 when negative). We show that an automaton returns the letter at position $n \in ℤ$ of the periodic point when fed with the representation of $n$. The numeration system naturally extends to $ℤ^d$. We give an equivalent characterization of the numeration system in terms of a total order on a regular language. Lastly, using particular periodic points, we recover the well-known two's complement numeration system and the Fibonacci analogue of the two's complement numeration system.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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