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- W4322760104 abstract "We extend the well-known Dumont--Thomas numeration system to $mathbb{Z}$ by considering two-sided periodic points of a substitution, thus allowing us to represent any integer in $mathbb{Z}$ by a finite word (starting with $mathtt{0}$ when nonnegative and with $mathtt{1}$ when negative). We show that an automaton returns the letter at position $ninmathbb{Z}$ of the periodic point when fed with the representation of $n$. The numeration system naturally extends to $mathbb{Z}^d$. 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." @default.
- W4322760104 created "2023-03-03" @default.
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- W4322760104 date "2023-02-28" @default.
- W4322760104 modified "2023-10-18" @default.
- W4322760104 title "Dumont--Thomas numeration systems for $mathbb{Z}$" @default.
- W4322760104 doi "https://doi.org/10.48550/arxiv.2302.14481" @default.
- W4322760104 hasPublicationYear "2023" @default.
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