In this text, we prove the existence of an asymptotic growth rate of the number of dominating sets (and variants) on finite rectangular grids, when the dimensions of the grid grow to infinity. Moreover, we provide, for each of the variants, an algorithm which computes the growth rate. We also give bounds on these rates provided by a computer program.

中文翻译：

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方格主导集的渐近增长率：一种符号动力学方法

在本文中，当网格的尺寸增长到无穷大时，我们证明了有限矩形网格上支配集（和变体）数量的渐近增长率。此外，我们为每个变体提供一种计算增长率的算法。我们还对计算机程序提供的这些速率进行了限制。