Abstract
Motivated by the study of Fibonacci-like Wang shifts, we define a numeration system for \(\mathbb {Z}\) and \(\mathbb {Z}^2\) based on the binary alphabet \(\{0,1\}\). We introduce a set of 16 Wang tiles that admits a valid tiling of the plane described by a deterministic finite automaton taking as input the representation of a position \((m,n)\in \mathbb {Z}^2\) and outputting a Wang tile.
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Notes
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In contrast to [BR10] we omit the coding as it is the identity map.
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Note that from now on, \(\sigma \) denotes the shift action and not a morphism.
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Acknowledgements
This work was supported by the Agence Nationale de la Recherche through the project Codys (ANR-18-CE40-0007).
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Labbé, S., Lepšová, J. (2021). A Numeration System for Fibonacci-Like Wang Shifts. In: Lecroq, T., Puzynina, S. (eds) Combinatorics on Words. WORDS 2021. Lecture Notes in Computer Science(), vol 12847. Springer, Cham. https://doi.org/10.1007/978-3-030-85088-3_9
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DOI: https://doi.org/10.1007/978-3-030-85088-3_9
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