On Countable SFT Covers of Sparse Multidimensional Shift Spaces

Ilkka Törmä

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arXiv · 2409.14967

On Countable SFT Covers of Sparse Multidimensional Shift Spaces

Ilkka Törmä

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Abstract

A multidimensional sofic shift is called countably covered if it has an SFT cover containing only countably many configurations. In contrast to the one-dimensional setting, not all countable sofic shifts are countably covered. We investigate the existence of countable covers for gap width shifts, where the number of nonzero symbols in a configuration is bounded by a function of the minimum distance between two such symbols. As our main results, we characterize those one-dimensional gap width shifts whose two-dimensional lift is a countably covered sofic shift, and show that a large class of two-dimensional gap width shifts are countably covered.

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Ilkka Törmä. 2024-09-23. On Countable SFT Covers of Sparse Multidimensional Shift Spaces. https://arxiv.org/abs/2409.14967

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