论文标题
在周期性分解和非专业线上
On Periodic Decompositions and Nonexpansive Lines
论文作者
论文摘要
在他的博士学位论文，米哈尔·萨巴多斯（Michal Szabados）猜想，对于不完全周期性的配置而具有最小的周期性分解，非专用线正是在这种分解中包含某些周期构型的周期的线。在本文中，我们研究了Szabados的猜想。首先，我们表明我们可以考虑最小的周期性分解，其中每个周期性配置在有限字母上定义。然后，我们证明Szabados的猜想适用于广泛的配置，其中包括所有并非完全周期性的低凸模式复杂性配置。
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.
