On Periodic Decompositions and Nonexpansive Lines

Cleber Fernando Colle

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arXiv · 2204.06658

On Periodic Decompositions and Nonexpansive Lines

Cleber Fernando Colle

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Abstract

In his Ph.D. thesis, Michal Szabados conjectured that for a not fully periodic configuration with a minimal periodic decomposition the nonexpansive lines are exactly the lines that contain a period for some periodic configuration in such decomposition. In this paper, we study Szabados's conjecture. First, we show that we may consider a minimal periodic decomposition where each periodic configuration is defined on a finite alphabet. Then we prove that Szabados's conjecture holds for a wide class of configurations, which includes all not fully periodic low convex pattern complexity configurations.

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Cleber Fernando Colle. 2022-04-13. On Periodic Decompositions and Nonexpansive Lines. https://arxiv.org/abs/2204.06658

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